# Simple Equation

## Exercise 4.2

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

(a) `x – 1 = 0`

**Answer:** Step 1: The number 1 will be moved to RHS of equation with suitable change in sign.

So, `x – 1 = 0`

Or, `x = 0 + 1 = 1`

(b) `x + 1 = 0`

**Answer:** Step 1: The number 1 will be moved to RHS of equation with suitable change in sign.

So, `x + 1 = 0`

Or, `x = 0 – 1 = - 1`

(c) `x – 1 = 5`

**Answer:** The number 1 will be moved to RHS of equation with suitable change in sign.

So, `x – 1 = 5`

Or, `x = 5 + 1 = 6`

(d) `x + 6 = 2`

**Answer:** The number 6 will be moved to RHS of equation with suitable change in sign.

So, `x + 6 = 2`

Or, `x = 2 – 6 = - 4`

(e) `y – 4 = - 7`

**Answer:** The number 4 will be moved to RHS of equation with suitable change in sign.

So, `y – 4 = 7`

Or, `y = 7 + 4 = 11`

(e) `y – 4 = 4`

**Answer:** The number 4 will be moved to RHS of equation with suitable change in sign.

So, `y – 4 = 4`

Or, `y = 4 + 4 = 8`

(f) `y + 4 = 4`

**Answer:** The number 4 will be moved to RHS of equation with suitable change in sign.

So, `y + 4 = 4`

Or, `y = 4 – 4 = 0`

(g) `y + 4 = - 4`

**Answer:** The number 4 will be moved to RHS of equation with suitable change in sign.

So, `y + 4 = - 4`

Or, `y = - 4 – 4 = - 8`

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

**Answer:** In following questions, the number from LHS will be moved to RHS of equation. Sign of multiplication will be changed to sign of division. Similarly, sign of division will be changed to sign of multiplication to solve the equation.

(a) `3l = 42`

**Answer:** `3l = 42`

Or, `l = 42 ÷ 3 = 14`

(b) `b/2 = 5`

**Answer:** `b/2 = 5`

Or, `b = 5 xx 2 = 10`

(c) `p/7 = 4`

**Answer:** `p/7 = 4`

Or, `p = 4 xx 7 = 28`

(d) `4x = 25`

**Answer:** `4x = 25`

Or, `x = 25 ÷ 4 = 6.25`

(e) `8y = 36`

**Answer:** `8y = 36`

Or, `y = 36 ÷ 8 = 4.5`

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

**Answer:** `z/3 = 5/4`

Or, `z = (5 xx 3) ÷ 4 = 3.75`

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

**Answer:** `a/5 = (7)/(15)`

Or, `a = (7 xx 5) ÷ 15 = 7/3`

(h) `20 t = - 10`

**Answer:** `20t = - 10`

Or, `t = - 10 ÷ 20 = -0.5`

**Question 3:** Solve the following equations:

(a) `3n – 2 = 46`

**Answer:** `3n – 2 = 46`

Or, `3n = 46 + 2 = 48`

Or, `n = 48 ÷ 3 = 16`

(b) `5m + 7 = 17`

**Answer:** `5m + 7 = 17`

Or, `5m = 17 + 7 = 24`

Or, `m = 24 ÷ 5 =4.8`

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

**Answer:** `(20p)/(3) = 40`

Or, `20p = 40 xx 3 = 120`

Or, `p = 120 ÷ 20 = 6`

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

**Answer:** `(3p)/(10) = 6`

Or, `3p = 6 xx 10 = 60`

Or, `p = 60 ÷ 3 = 20`

**Question 4:** Solve the following equations:

(a) `10 p = 100`

**Answer:** `10 p = 100`

Or, `p = 100 ÷ 10 = 10`

(b) `10p + 10 = 100`

**Answer:** `10p + 10 = 100`

Or, `10p = 100 – 10 = 90`

Or, `p = 90 ÷ 10 = 10`

(c) `p/4 = 5`

**Answer:** `p/4 = 5`

Or, `p 5 xx 4 = 20`

(d) `p/3 = 5`

**Answer:** `p/3 = 5`

Or, `p = 5 xx 3 = 15`

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

**Answer:** `(3p)/(4) = 6`

Or, `3p = 6 xx 4 = 24`

Or, `p = 24 ÷ 3 = 8`

(f) `3s = - 9`

**Answer:** `3s = - 9`

Or, `s = - 9 ÷ 3 = - 3`

(g) `3s + 12 = 0`

**Answer:** `3s + 12 = 0`

Or, `3s = 0 – 12 = - 12`

Or, `s = - 12 ÷ 3 = - 4`

(h) `3s = 0`

**Answer:** `3s = 0`

Or, `s = 0 ÷ 3 = 0`

(i) `2q = 6`

**Answer:** `2q = 6`

Or, `q = 6 ÷ 2 = 3`

(j) `2q – 6 = 0`

**Answer:** `2q – 6 = 0`

Or, `2q = 0 + 6 = 6`

Or, `q = 6 ÷ 2 = 3`

(k) `2q + 6 = 12`

**Answer:** `2q + 6 = 12`

Or, `2q = 12 – 6 = 6`

Or, `q = 6 ÷ 2 = 3`