# Chapter – 4: Simple Equations

# Exercise 4.1

**1. Complete the last column of the table.**

S. No. | Equation | Value | Say, whether the equation is satisfied. (Yes/No) |

(i) | x + 3 = 0 | x = 3 | |

(ii) | x + 3 = 0 | x = 0 | |

(iii) | x + 3 = 0 | x = -3 | |

(iv) | x – 7 = 1 | x = 7 | |

(v) | x – 7 = 1 | x = 8 | |

(vi) | 5x = 25 | x = 0 | |

(vii) | 5x = 25 | x = 5 | |

(viii) | 5x = 25 | x = -5 | |

(ix) | (m/3) = 2 | m = – 6 | |

(x) | (m/3) = 2 | m = 0 | |

(xi) | (m/3) = 2 | m = 6 |

**Solution:**

(i) x + 3 = 0

LHS = x + 3

By substituting the value of x = 3

Then,

LHS = 3 + 3 = 6

By comparing LHS and RHS

LHS ≠ RHS

∴No, the equation is not satisfied.

(ii) x + 3 = 0

LHS = x + 3

By substituting the value of x = 0

Then,

LHS = 0 + 3 = 3

By comparing LHS and RHS

LHS ≠ RHS

∴No, the equation is not satisfied.

(iii) x + 3 = 0

LHS = x + 3

By substituting the value of x = – 3

Then,

LHS = – 3 + 3 = 0

By comparing LHS and RHS

LHS = RHS

∴Yes, the equation is satisfied

(iv) x – 7 = 1

LHS = x – 7

By substituting the value of x = 7

Then,

LHS = 7 – 7 = 0

By comparing LHS and RHS

LHS ≠ RHS

∴No, the equation is not satisfied

(v) x – 7 = 1

LHS = x – 7

By substituting the value of x = 8

Then,

LHS = 8 – 7 = 1

By comparing LHS and RHS

LHS = RHS

∴Yes, the equation is satisfied.

(vi) 5x = 25

LHS = 5x

By substituting the value of x = 0

Then,

LHS = 5 × 0 = 0

By comparing LHS and RHS

LHS ≠ RHS

∴No, the equation is not satisfied.

(vii) 5x = 25

LHS = 5x

By substituting the value of x = 5

Then,

LHS = 5 × 5 = 25

By comparing LHS and RHS

LHS = RHS

∴Yes, the equation is satisfied.

(viii) 5x = 25

LHS = 5x

By substituting the value of x = -5

Then,

LHS = 5 × (-5) = – 25

By comparing LHS and RHS

LHS ≠ RHS

∴No, the equation is not satisfied.

(ix) m/3 = 2

LHS = m/3

By substituting the value of m = – 6

Then,

LHS = -6/3 = – 2

By comparing LHS and RHS

LHS ≠ RHS

∴No, the equation is not satisfied.

(x) m/3 = 2

LHS = m/3

By substituting the value of m = 0

Then,

LHS = 0/3 = 0

By comparing LHS and RHS

LHS ≠ RHS

∴No, the equation is not satisfied.

(xi) m/3 = 2

LHS = m/3

By substituting the value of m = 6

Then,

LHS = 6/3 = 2

By comparing LHS and RHS

LHS = RHS

∴Yes, the equation is satisfied.

S. No. | Equation | Value | Say, whether the equation is satisfied. (Yes/No) |

(i) | x + 3 = 0 | x = 3 | No |

(ii) | x + 3 = 0 | x = 0 | No |

(iii) | x + 3 = 0 | x = -3 | Yes |

(iv) | x – 7 = 1 | x = 7 | No |

(v) | x – 7 = 1 | x = 8 | Yes |

(vi) | 5x = 25 | x = 0 | No |

(vii) | 5x = 25 | x = 5 | Yes |

(viii) | 5x = 25 | x = -5 | No |

(ix) | (m/3) = 2 | m = – 6 | No |

(x) | (m/3) = 2 | m = 0 | No |

(xi) | (m/3) = 2 | m = 6 | Yes |

**2. Check whether the value given in the brackets is a solution to the given equation or not:**

**(a) n + 5 = 19 (n = 1)**

**Solution:**

LHS = n + 5

By substituting the value of n = 1

Then,

LHS = n + 5

= 1 + 5

= 6

By comparing LHS and RHS

6 ≠ 19

LHS ≠ RHS

Hence, the value of n = 1 is not a solution to the given equation n + 5 = 19.

**(b) 7n + 5 = 19 (n = – 2)**

**Solution:**

LHS = 7n + 5

By substituting the value of n = -2

Then,

LHS = 7n + 5

= (7 × (-2)) + 5

= – 14 + 5

= – 9

By comparing LHS and RHS

-9 ≠ 19

LHS ≠ RHS

Hence, the value of n = -2 is not a solution to the given equation 7n + 5 = 19.

**(c) 7n + 5 = 19 (n = 2)**

**Solution:**

LHS = 7n + 5

By substituting the value of n = 2

Then,

LHS = 7n + 5

= (7 × (2)) + 5

= 14 + 5

= 19

By comparing LHS and RHS

19 = 19

LHS = RHS

Hence, the value of n = 2 is a solution to the given equation 7n + 5 = 19.

**(d) 4p – 3 = 13 (p = 1)**

**Solution:**

LHS = 4p – 3

By substituting the value of p = 1

Then,

LHS = 4p – 3

= (4 × 1) – 3

= 4 – 3

= 1

By comparing LHS and RHS

1 ≠ 13

LHS ≠ RHS

Hence, the value of p = 1 is not a solution to the given equation 4p – 3 = 13.

**(e) 4p – 3 = 13 (p = – 4)**

**Solution:**

LHS = 4p – 3

By substituting the value of p = – 4

Then,

LHS = 4p – 3

= (4 × (-4)) – 3

= -16 – 3

= -19

By comparing LHS and RHS

-19 ≠ 13

LHS ≠ RHS

Hence, the value of p = -4 is not a solution to the given equation 4p – 3 = 13.

**(f) 4p – 3 = 13 (p = 0)**

**Solution:**

LHS = 4p – 3

By substituting the value of p = 0

Then,

LHS = 4p – 3

= (4 × 0) – 3

= 0 – 3

= -3

By comparing LHS and RHS

– 3 ≠ 13

LHS ≠ RHS

Hence, the value of p = 0 is not a solution to the given equation 4p – 3 = 13.

**3. Solve the following equations by trial and error method:**

**(i) 5p + 2 = 17**

**Solution:**

LHS = 5p + 2

By substituting the value of p = 0

Then,

LHS = 5p + 2

= (5 × 0) + 2

= 0 + 2

= 2

By comparing LHS and RHS

2 ≠ 17

LHS ≠ RHS

Hence, the value of p = 0 is not a solution to the given equation.

Let, p = 1

LHS = 5p + 2

= (5 × 1) + 2

= 5 + 2

= 7

By comparing LHS and RHS

7 ≠ 17

LHS ≠ RHS

Hence, the value of p = 1 is not a solution to the given equation.

Let, p = 2

LHS = 5p + 2

= (5 × 2) + 2

= 10 + 2

= 12

By comparing LHS and RHS

12 ≠ 17

LHS ≠ RHS

Hence, the value of p = 2 is not a solution to the given equation.

Let, p = 3

LHS = 5p + 2

= (5 × 3) + 2

= 15 + 2

= 17

By comparing LHS and RHS

17 = 17

LHS = RHS

Hence, the value of p = 3 is a solution to the given equation.

**(ii) 3m – 14 = 4**

**Solution:**

LHS = 3m – 14

By substituting the value of m = 3

Then,

LHS = 3m – 14

= (3 × 3) – 14

= 9 – 14

= – 5

By comparing LHS and RHS

-5 ≠ 4

LHS ≠ RHS

Hence, the value of m = 3 is not a solution to the given equation.

Let, m = 4

LHS = 3m – 14

= (3 × 4) – 14

= 12 – 14

= – 2

By comparing LHS and RHS

-2 ≠ 4

LHS ≠ RHS

Hence, the value of m = 4 is not a solution to the given equation.

Let, m = 5

LHS = 3m – 14

= (3 × 5) – 14

= 15 – 14

= 1

By comparing LHS and RHS

1 ≠ 4

LHS ≠ RHS

Hence, the value of m = 5 is not a solution to the given equation.

Let, m = 6

LHS = 3m – 14

= (3 × 6) – 14

= 18 – 14

= 4

By comparing LHS and RHS

4 = 4

LHS = RHS

Hence, the value of m = 6 is a solution to the given equation.

**4. Write equations for the following statements:**

**(i) The sum of numbers x and 4 is 9.**

**Solution:**

The above statement can be written in the equation form as,

= x + 4 = 9

**(ii) 2 subtracted from y is 8.**

**Solution:**

The above statement can be written in the equation form as,

= y – 2 = 8

**(iii) Ten times a is 70.**

**Solution:**

The above statement can be written in the equation form as,

= 10a = 70

**(iv) The number b divided by 5 gives 6.**

**Solution:**

The above statement can be written in the equation form as,

= (b/5) = 6

**(v) Three-fourth of t is 15.**

**Solution:**

The above statement can be written in the equation form as,

= ¾t = 15

**(vi) Seven times m plus 7 gets you 77.**

**Solution:**

The above statement can be written in the equation form as,

Seven times m is 7m

= 7m + 7 = 77

**(vii) One-fourth of a number x minus 4 gives 4.**

**Solution:**

The above statement can be written in the equation form as,

One-fourth of a number x is x/4

= x/4 – 4 = 4

**(viii) If you take away 6 from 6 times y, you get 60.**

**Solution:**

The above statement can be written in the equation form as,

6 times of y is 6y

= 6y – 6 = 60

**(ix) If you add 3 to one-third of z, you get 30.**

**Solution:**

The above statement can be written in the equation form as,

One-third of z is z/3

= 3 + z/3 = 30

**5. Write the following equations in statement forms:**

**(i) p + 4 = 15**

**Solution:**

The sum of numbers p and 4 is 15.

**(ii) m – 7 = 3**

**Solution:**

7 subtracted from m is 3.

**(iii) 2m = 7**

**Solution:**

Twice of number m is 7.

**(iv) m/5 = 3**

**Solution:**

The number m divided by 5 gives 3.

**(v) (3m)/5 = 6**

**Solution:**

Three-fifth of m is 6.

**(vi) 3p + 4 = 25**

**Solution:**

Three times p plus 4 gives you 25.

**(vii) 4p – 2 = 18**

**Solution:**

Four times p minus 2 gives you 18.

**(viii) p/2 + 2 = 8**

**Solution:**

If you add half of a number p to 2, you get 8.

**6. Set up an equation in the following cases:**

**(i) Irfan says that he has 7 marbles more than five times the marbles Parmit has. Irfan has 37 marbles. (Take m to be the number of Permit’s marbles.)**

**Solution:**

From the question it is given that,

Number of Parmit’s marbles = m

Then,

Irfan has 7 marbles more than five times the marbles Parmit has

= 5 × Number of Parmit’s marbles + 7 = Total number of marbles Irfan having

= (5 × m) + 7 = 37

= 5m + 7 = 37

**(ii) Laxmi’s father is 49 years old. He is 4 years older than three times Laxmi’s age. (Take Laxmi’s age to be y years.)**

**Solution:**

From the question it is given that,

Let Laxmi’s age to be = y years old

Then,

Lakshmi’s father is 4 years older than three times of her age

= 3 × Laxmi’s age + 4 = Age of Lakshmi’s father

= (3 × y) + 4 = 49

= 3y + 4 = 49

**(iii) The teacher tells the class that the highest marks obtained by a student in her class is twice the lowest marks plus 7. The highest score is 87. (Take the lowest score to be l.)**

**Solution:**

From the question it is given that,

Highest score in the class = 87

Let lowest score be l

= 2 × Lowest score + 7 = Highest score in the class

= (2 × l) + 7 = 87

= 2l + 7 = 87

**(iv) In an isosceles triangle, the vertex angle is twice either base angle. (Let the base angle be b in degrees. Remember that the sum of angles of a triangle is 180 degrees).**

**Solution:**

From the question it is given that,

We know that, the sum of angles of a triangle is 180^{o}

Let base angle be b

Then,

Vertex angle = 2 × base angle = 2b

= b + b + 2b = 180^{o}

= 4b = 180^{o}

# Exercise 4.2

**1. Give first the step you will use to separate the variable and then solve the equation:**

**(a) x – 1 = 0**

**Solution:**

We have to add 1 to both the side of given equation,

Then we get,

= x – 1 + 1 = 0 + 1

= x = 1

**(b) x + 1 = 0**

**Solution:**

We have to subtract 1 to both the side of given equation,

Then we get,

= x + 1 – 1 = 0 – 1

= x = – 1

**(c) x – 1 = 5**

**Solution:**

We have to add 1 to both the side of given equation,

Then we get,

= x – 1 + 1 = 5 + 1

= x = 6

**(d) x + 6 = 2**

**Solution:**

We have to subtract 6 to both the side of given equation,

Then we get,

= x + 6 – 6 = 2 – 6

= x = – 4

**(e) y – 4 = – 7**

**Solution:**

We have to add 4 to both the side of given equation,

Then we get,

= y – 4 + 4 = – 7 + 4

= y = – 3

**(f) y – 4 = 4**

**Solution:**

We have to add 4 to both the side of given equation,

Then we get,

= y – 4 + 4 = 4 + 4

= y = 8

**(g) y + 4 = 4**

**Solution:**

We have to subtract 4 to both the side of given equation,

Then we get,

= y + 4 – 4 = 4 – 4

= y = 0

**(h) y + 4 = – 4**

**Solution:**

We have to subtract 4 to both the side of given equation,

Then we get,

= y + 4 – 4 = – 4 – 4

= y = – 8

**2. Give first the step you will use to separate the variable and then solve the equation:**

**(a) 3l = 42**

**Solution:**

Now we have to divide both sides of the equation by 3,

Then we get,

= 3l/3 = 42/3

= l = 14

**(b) b/2 = 6**

**Solution:**

Now we have to multiply both sides of the equation by 2,

Then we get,

= b/2 × 2= 6 × 2

= b = 12

**(c) p/7 = 4**

**Solution:**

Now we have to multiply both sides of the equation by 7,

Then we get,

= p/7 × 7= 4 × 7

= p = 28

**(d) 4x = 25**

**Solution:**

Now we have to divide both sides of the equation by 4,

Then we get,

= 4x/4 = 25/4

= x = 25/4

**(e) 8y = 36**

**Solution:**

Now we have to divide both sides of the equation by 8,

Then we get,

= 8y/8 = 36/8

= x = 9/2

**(f) (z/3) = (5/4)**

**Solution:**

Now we have to multiply both sides of the equation by 3,

Then we get,

= (z/3) × 3 = (5/4) × 3

= x = 15/4

**(g) (a/5) = (7/15)**

**Solution:**

Now we have to multiply both sides of the equation by 5,

Then we get,

= (a/5) × 5 = (7/15) × 5

= a = 7/3

**(h) 20t = – 10**

**Solution:**

Now we have to divide both sides of the equation by 20,

Then we get,

= 20t/20 = -10/20

= x = – ½

**3. Give the steps you will use to separate the variable and then solve the equation:**

**(a) 3n – 2 = 46**

**Solution:**

First we have to add 2 to the both sides of the equation,

Then, we get,

= 3n – 2 + 2 = 46 + 2

= 3n = 48

Now,

We have to divide both sides of the equation by 3,

Then, we get,

= 3n/3 = 48/3

= n = 16

**(b) 5m + 7 = 17**

**Solution:**

First we have to subtract 7 to the both sides of the equation,

Then, we get,

= 5m + 7 – 7 = 17 – 7

= 5m = 10

Now,

We have to divide both sides of the equation by 5,

Then, we get,

= 5m/5 = 10/5

= m = 2

**(c) 20p/3 = 40**

**Solution:**

First we have to multiply both sides of the equation by 3,

Then, we get,

= (20p/3) × 3 = 40 × 3

= 20p = 120

Now,

We have to divide both sides of the equation by 20,

Then, we get,

= 20p/20 = 120/20

= p = 6

**(d) 3p/10 = 6**

**Solution:**

First we have to multiply both sides of the equation by 10,

Then, we get,

= (3p/10) × 10 = 6 × 10

= 3p = 60

Now,

We have to divide both sides of the equation by 3,

Then, we get,

= 3p/3 = 60/3

= p = 20

**4. Solve the following equations:**

**(a) 10p = 100**

**Solution:**

Now,

We have to divide both sides of the equation by 10,

Then, we get,

= 10p/10 = 100/10

= p = 10

**(b) 10p + 10 = 100**

**Solution:**

First we have to subtract 10 to the both sides of the equation,

Then, we get,

= 10p + 10 – 10 = 100 – 10

= 10p = 90

Now,

We have to divide both sides of the equation by 10,

Then, we get,

= 10p/10 = 90/10

= p = 9

**(c) p/4 = 5**

**Solution:**

Now,

We have to multiply both sides of the equation by 4,

Then, we get,

= p/4 × 4 = 5 × 4

= p = 20

**(d) – p/3 = 5**

**Solution:**

Now,

We have to multiply both sides of the equation by – 3,

Then, we get,

= – p/3 × (- 3) = 5 × (- 3)

= p = – 15

**(e) 3p/4 = 6**

**Solution:**

First we have to multiply both sides of the equation by 4,

Then, we get,

= (3p/4) × (4) = 6 × 4

= 3p = 24

Now,

We have to divide both sides of the equation by 3,

Then, we get,

= 3p/3 = 24/3

= p = 8

**(f) 3s = – 9**

**Solution:**

Now,

We have to divide both sides of the equation by 3,

Then, we get,

= 3s/3 = -9/3

= s = -3

**(g) 3s + 12 = 0**

**Solution:**

First we have to subtract 12 to the both sides of the equation,

Then, we get,

= 3s + 12 – 12 = 0 – 12

= 3s = -12

Now,

We have to divide both sides of the equation by 3,

Then, we get,

= 3s/3 = -12/3

= s = – 4

**(h) 3s = 0**

**Solution:**

Now,

We have to divide both sides of the equation by 3,

Then, we get,

= 3s/3 = 0/3

= s = 0

**(i) 2q = 6**

**Solution:**

Now,

We have to divide both sides of the equation by 2,

Then, we get,

= 2q/2 = 6/2

= q = 3

**(j) 2q – 6 = 0**

**Solution:**

First we have to add 6 to the both sides of the equation,

Then, we get,

= 2q – 6 + 6 = 0 + 6

= 2q = 6

Now,

We have to divide both sides of the equation by 2,

Then, we get,

= 2q/2 = 6/2

= q = 3

**(k) 2q + 6 = 0**

**Solution:**

First we have to subtract 6 to the both sides of the equation,

Then, we get,

= 2q + 6 – 6 = 0 – 6

= 2q = – 6

Now,

We have to divide both sides of the equation by 2,

Then, we get,

= 2q/2 = – 6/2

= q = – 3

**(l) 2q + 6 = 12**

**Solution:**

First we have to subtract 6 to the both sides of the equation,

Then, we get,

= 2q + 6 – 6 = 12 – 6

= 2q = 6

Now,

We have to divide both sides of the equation by 2,

Then, we get,

= 2q/2 = 6/2

= q = 3

# Exercise 4.3

**1. Solve the following equations:**

**(a) 2y + (5/2) = (37/2)**

**Solution:**

By transposing (5/2) from LHS to RHS it becomes -5/2

Then,

= 2y = (37/2) – (5/2)

= 2y = (37-5)/2

= 2y = 32/2

Now,

Divide both side by 2,

= 2y/2 = (32/2)/2

= y = (32/2) × (1/2)

= y = 32/4

= y = 8

**(b) 5t + 28 = 10**

**Solution:**

By transposing 28 from LHS to RHS it becomes -28

Then,

= 5t = 10 – 28

= 5t = – 18

Now,

Divide both side by 5,

= 5t/5= -18/5

= t = -18/5

**(c) (a/5) + 3 = 2**

**Solution:**

By transposing 3 from LHS to RHS it becomes -3

Then,

= a/5 = 2 – 3

= a/5 = – 1

Now,

Multiply both side by 5,

= (a/5) × 5= -1 × 5

= a = -5

**(d) (q/4) + 7 = 5**

**Solution:**

By transposing 7 from LHS to RHS it becomes -7

Then,

= q/4 = 5 – 7

= q/4 = – 2

Now,

Multiply both side by 4,

= (q/4) × 4= -2 × 4

= a = -8

**(e) (5/2) x = -5**

**Solution:**

First we have to multiply both the side by 2,

= (5x/2) × 2 = – 5 × 2

= 5x = – 10

Now,

We have to divide both the side by 5,

Then we get,

= 5x/5 = -10/5

= x = -2

**(f) (5/2) x = 25/4**

**Solution:**

First we have to multiply both the side by 2,

= (5x/2) × 2 = (25/4) × 2

= 5x = (25/2)

Now,

We have to divide both the side by 5,

Then we get,

= 5x/5 = (25/2)/5

= x = (25/2) × (1/5)

= x = (5/2)

**(g) 7m + (19/2) = 13**

**Solution:**

By transposing (19/2) from LHS to RHS it becomes -19/2

Then,

= 7m = 13 – (19/2)

= 7m = (26 – 19)/2

= 7m = 7/2

Now,

Divide both side by 7,

= 7m/7 = (7/2)/7

= m = (7/2) × (1/7)

= m = ½

**(h) 6z + 10 = – 2**

**Solution:**

By transposing 10 from LHS to RHS it becomes – 10

Then,

= 6z = -2 – 10

= 6z = – 12

Now,

Divide both side by 6,

= 6z/6 = -12/6

= m = – 2

**(i) (3/2) l = 2/3**

**Solution:**

First we have to multiply both the side by 2,

= (3l/2) × 2 = (2/3) × 2

= 3l = (4/3)

Now,

We have to divide both the side by 3,

Then we get,

= 3l/3 = (4/3)/3

= l = (4/3) × (1/3)

= x = (4/9)

**(j) (2b/3) – 5 = 3**

**Solution:**

By transposing -5 from LHS to RHS it becomes 5

Then,

= 2b/3 = 3 + 5

= 2b/3 = 8

Now,

Multiply both side by 3,

= (2b/3) × 3= 8 × 3

= 2b = 24

And,

Divide both side by 2,

= 2b/2 = 24/2

= b = 12

**2. Solve the following equations:**

**(a) 2(x + 4) = 12**

**Solution:**

Let us divide both the side by 2,

= (2(x + 4))/2 = 12/2

= x + 4 = 6

By transposing 4 from LHS to RHS it becomes -4

= x = 6 – 4

= x = 2

**(b) 3(n – 5) = 21**

**Solution:**

Let us divide both the side by 3,

= (3(n – 5))/3 = 21/3

= n – 5 = 7

By transposing -5 from LHS to RHS it becomes 5

= n = 7 + 5

= n = 12

**(c) 3(n – 5) = – 21**

**Solution:**

Let us divide both the side by 3,

= (3(n – 5))/3 = – 21/3

= n – 5 = -7

By transposing -5 from LHS to RHS it becomes 5

= n = – 7 + 5

= n = – 2

**(d) – 4(2 + x) = 8**

**Solution:**

Let us divide both the side by -4,

= (-4(2 + x))/ (-4) = 8/ (-4)

= 2 + x = -2

By transposing 2 from LHS to RHS it becomes – 2

= x = -2 – 2

= x = – 4

**(e) 4(2 – x) = 8**

**Solution:**

Let us divide both the side by 4,

= (4(2 – x))/ 4 = 8/ 4

= 2 – x = 2

By transposing 2 from LHS to RHS it becomes – 2

= – x = 2 – 2

= – x = 0

= x = 0

**3. Solve the following equations:**

**(a) 4 = 5(p – 2)**

**Solution:**

Let us divide both the side by 5,

= 4/5 = (5(p – 2))/5

= 4/5 = p -2

By transposing – 2 from RHS to LHS it becomes 2

= (4/5) + 2 = p

= (4 + 10)/ 5 = p

= p = 14/5

**(b) – 4 = 5(p – 2)**

**Solution:**

Let us divide both the side by 5,

= – 4/5 = (5(p – 2))/5

= – 4/5 = p -2

By transposing – 2 from RHS to LHS it becomes 2

= – (4/5) + 2 = p

= (- 4 + 10)/ 5 = p

= p = 6/5

**(c) 16 = 4 + 3(t + 2)**

**Solution:**

By transposing 4 from RHS to LHS it becomes – 4

= 16 – 4 = 3(t + 2)

= 12 = 3(t + 2)

Let us divide both the side by 3,

= 12/3 = (3(t + 2))/ 3

= 4 = t + 2

By transposing 2 from RHS to LHS it becomes – 2

= 4 – 2 = t

= t = 2

**(d) 4 + 5(p – 1) =34**

**Solution:**

By transposing 4 from LHS to RHS it becomes – 4

= 5(p – 1) = 34 – 4

= 5(p – 1) = 30

Let us divide both the side by 5,

= (5(p – 1))/ 5 = 30/5

= p – 1 = 6

By transposing – 1 from RHS to LHS it becomes 1

= p = 6 + 1

= p = 7

**(e) 0 = 16 + 4(m – 6)**

**Solution:**

By transposing 16 from RHS to LHS it becomes – 16

= 0 – 16 = 4(m – 6)

= – 16 = 4(m – 6)

Let us divide both the side by 4,

= – 16/4 = (4(m – 6))/ 4

= – 4 = m – 6

By transposing – 6 from RHS to LHS it becomes 6

= – 4 + 6 = m

= m = 2

**4. (a) Construct 3 equations starting with x = 2**

**Solution:**

First equation is,

Multiply both side by 6

= 6x = 12 … [equation 1]

Second equation is,

Subtracting 4 from both side,

= 6x – 4 = 12 -4

= 6x – 4 = 8 … [equation 2]

Third equation is,

Divide both side by 6

= (6x/6) – (4/6) = (8/6)

= x – (4/6) = (8/6) … [equation 3]

**(b) Construct 3 equations starting with x = – 2**

**Solution:**

First equation is,

Multiply both side by 5

= 5x = -10 … [equation 1]

Second equation is,

Subtracting 3 from both side,

= 5x – 3 = – 10 – 3

= 5x – 3 = – 13 … [equation 2]

Third equation is,

Dividing both sides by 2

= (5x/2) – (3/2) = (-13/2) … [equation 3]

# Exercise 4.4

**1. Set up equations and solve them to find the unknown numbers in the following cases:**

**(a) Add 4 to eight times a number; you get 60.**

**Solution:**

Let us assume the required number be x

Eight times a number = 8x

The given above statement can be written in the equation form as,

= 8x + 4 = 60

By transposing 4 from LHS to RHS it becomes – 4

= 8x = 60 – 4

= 8x = 56

Divide both side by 8,

Then we get,

= (8x/8) = 56/8

= x = 7

**(b) One-fifth of a number minus 4 gives 3.**

**Solution:**

Let us assume the required number be x

One-fifth of a number = (1/5) x = x/5

The given above statement can be written in the equation form as,

= (x/5) – 4 = 3

By transposing – 4 from LHS to RHS it becomes 4

= x/5 = 3 + 4

= x/5 = 7

Multiply both side by 5,

Then we get,

= (x/5) × 5 = 7 × 5

= x = 35

**(c) If I take three-fourths of a number and add 3 to it, I get 21.**

**Solution:**

Let us assume the required number be x

Three-fourths of a number = (3/4) x

The given above statement can be written in the equation form as,

= (3/4) x + 3 = 21

By transposing 3 from LHS to RHS it becomes – 3

= (3/4) x = 21 – 3

= (3/4) x = 18

Multiply both side by 4,

Then we get,

= (3x/4) × 4 = 18 × 4

= 3x = 72

Then,

Divide both side by 3,

= (3x/3) = 72/3

= x = 24

**(d) When I subtracted 11 from twice a number, the result was 15.**

**Solution:**

Let us assume the required number be x

Twice a number = 2x

The given above statement can be written in the equation form as,

= 2x –11 = 15

By transposing -11 from LHS to RHS it becomes 11

= 2x = 15 + 11

= 2x = 26

Then,

Divide both side by 2,

= (2x/2) = 26/2

= x = 13

**(e) Munna subtracts thrice the number of notebooks he has from 50, he finds the result to be 8.**

**Solution:**

Let us assume the required number be x

Thrice the number = 3x

The given above statement can be written in the equation form as,

= 50 – 3x = 8

By transposing 50 from LHS to RHS it becomes – 50

= – 3x = 8 – 50

= -3x = – 42

Then,

Divide both side by -3,

= (-3x/-3) = – 42/-3

= x = 14

**(f) Ibenhal thinks of a number. If she adds 19 to it and divides the sum by 5, she will get 8.**

**Solution:**

Let us assume the required number be x

The given above statement can be written in the equation form as,

= (x + 19)/5 = 8

Multiply both side by 5,

= ((x + 19)/5) × 5 = 8 × 5

= x + 19 = 40

Then,

By transposing 19 from LHS to RHS it becomes – 19

= x = 40 – 19

= x = 21

**(g) Anwar thinks of a number. If he takes away 7 from 5/2 of the number, the result is 23.**

**Solution:**

Let us assume the required number be x

5/2 of the number = (5/2) x

The given above statement can be written in the equation form as,

= (5/2) x – 7 = 23

By transposing -7 from LHS to RHS it becomes 7

= (5/2) x = 23 + 7

= (5/2) x = 30

Multiply both side by 2,

= ((5/2) x) × 2 = 30 × 2

= 5x = 60

Then,

Divide both the side by 5

= 5x/5 = 60/5

= x = 12

**2. Solve the following:**

**(a) The teacher tells the class that the highest marks obtained by a student in her class is twice the lowest marks plus 7. The highest score is 87. What is the lowest score?**

**Solution:**

Let us assume the lowest score be x

From the question it is given that,

The highest score is = 87

Highest marks obtained by a student in her class is twice the lowest marks plus 7= 2x + 7

5/2 of the number = (5/2) x

The given above statement can be written in the equation form as,

Then,

= 2x + 7 = Highest score

= 2x + 7 = 87

By transposing 7 from LHS to RHS it becomes -7

= 2x = 87 – 7

= 2x = 80

Now,

Divide both the side by 2

= 2x/2 = 80/2

= x = 40

Hence, the lowest score is 40

**(b) In an isosceles triangle, the base angles are equal. The vertex angle is 40°.**

**What are the base angles of the triangle? (Remember, the sum of three angles of a triangle is 180°).**

**Solution:**

From the question it is given that,

We know that, the sum of angles of a triangle is 180^{o}

Let base angle be b

Then,

= b + b + 40^{o} = 180^{o}

= 2b + 40 = 180^{o}

By transposing 40 from LHS to RHS it becomes -40

= 2b = 180 – 40

= 2b = 140

Now,

Divide both the side by 2

= 2b/2 = 140/2

= b = 70^{o}

Hence, 70^{o} is the base angle of an isosceles triangle.

**(c) Sachin scored twice as many runs as Rahul. Together, their runs fell two short of a double century. How many runs did each one score?**

**Solution:**

Let us assume Rahul’s score be x

Then,

Sachin scored twice as many runs as Rahul is 2x

Together, their runs fell two short of a double century,

= Rahul’s score + Sachin’s score = 200 – 2

= x + 2x = 198

= 3x = 198

Divide both the side by 3,

= 3x/3 = 198/3

= x = 66

So, Rahul’s score is 66

And Sachin’s score is 2x = 2 × 66 = 132

**3. Solve the following:**

**(i) Irfan says that he has 7 marbles more than five times the marbles Parmit has.**

**Irfan has 37 marbles. How many marbles does Parmit have?**

**Solution:**

Let us assume number of Parmit’s marbles = m

From the question it is given that,

Then,

Irfan has 7 marbles more than five times the marbles Parmit has

= 5 × Number of Parmit’s marbles + 7 = Total number of marbles Irfan having

= (5 × m) + 7 = 37

= 5m + 7 = 37

By transposing 7 from LHS to RHS it becomes -7

= 5m = 37 – 7

= 5m = 30

Divide both the side by 5

= 5m/5 = 30/5

= m = 6

So, Permit has 6 marbles

**(ii) Laxmi’s father is 49 years old. He is 4 years older than three times Laxmi’s age.**

**What is Laxmi’s age?**

**Solution:**

Let Laxmi’s age to be = y years old

From the question it is given that,

Lakshmi’s father is 4 years older than three times of her age

= 3 × Laxmi’s age + 4 = Age of Lakshmi’s father

= (3 × y) + 4 = 49

= 3y + 4 = 49

By transposing 4 from LHS to RHS it becomes -4

= 3y = 49 – 4

= 3y = 45

Divide both the side by 3

= 3y/3 = 45/3

= y = 15

So, Lakshmi’s age is 15 years.

**(iii) People of Sundargram planted trees in the village garden. Some of the trees were fruit trees. The number of non-fruit trees were two more than three times the number of fruit trees. What was the number of fruit trees planted if the number of non-fruit trees planted was 77?**

**Solution:**

Let the number of fruit tress be f.

From the question it is given that,

3 × number of fruit trees + 2 = number of non-fruit trees

= 3f + 2 = 77

By transposing 2 from LHS to RHS it becomes -2

=3f = 77 – 2

= 3f = 75

Divide both the side by 3

= 3f/3 = 75/3

= f = 25

So, number of fruit tree was 25.

**4. Solve the following riddle:**

**I am a number,**

**Tell my identity!**

**Take me seven times over**

**And add a fifty!**

**To reach a triple century**

**You still need forty!**

**Solution:**

Let us assume the number be x.

Take me seven times over and add a fifty = 7x + 50

To reach a triple century you still need forty = (7x + 50) + 40 = 300

= 7x + 50 + 40 = 300

= 7x + 90 = 300

By transposing 90 from LHS to RHS it becomes -90

= 7x = 300 – 90

= 7x = 210

Divide both side by 7

= 7x/7 = 210/7

= x = 30

Hence the number is 30.

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