Page 48 - Maths Skills - 7

46 Maths

putting n = 2, LHS = 4 × 2 – 12 RHS = 8 putting n = 4, LHS = 4 × 4 – 12 RHS = 8
= 8 – 12 = 16 – 12
= – 4 = 4
Since, LHS ≠ RHS Since, LHS ≠ RHS
Hence, n = 2 is not the solution. Hence, n = 4 is not the solution.
putting n = 3, LHS = 4 × 3 – 12 RHS = 8 Putting n = 5, LHS = 4 × 5 – 12 RHS = 8
= 12 – 12 = 20 – 12
= 0 = 8
Since, LHS ≠ RHS Since, LHS = RHS
Hence, n = 3 is not the solution.
Hence, n = 5 is the solution of the given equation.

As you can see this method is not very convenient to obtain the solution, let us learn the other method.

Systematic Method
The rules for this method are:
(a) When we add or subtract the same number on both sides of the equation, it still holds true.

(b) When we multiply or divide both sides of the equation by the same non-zero number, it still holds true.
It is something like balancing both sides to get the solution.
For example, let us solve 3m – 4 = 2 Fact-o-meter

⇒ 3m – 4 + 4 = 2 + 4 (Adding 4 to both sides)
A balanced equation is like a
⇒ 3m = 6
weighing balance with equal
3 m 6 weights in its two pans.
⇒ 3 = 3 (Dividing both sides by 3)

⇒ m = 2 Hence, m = 2 is the solution of the given equation.
Let us learn more through examples.

Let’s Attempt

Example 1: Write the steps to separate the variable and then solve the following equations:
3 p
(i) 13p – 4 = 61 (ii) 4 – 8 = 1 (iii) 9t = 126 (iv) 2m + 6 = 12
3 p
Solution: (i) 13p – 4 = 61 (ii) 4 – 8 = 1

Adding 4 to both sides Adding 8 to both sides
3 p
13 p – 4 + 4 = 61 + 4 4 – 8 + 8 = 1 + 8
⇒ 13p = 65 ⇒ 3 4 p = 9

Dividing both sides by 13 Multiplying both sides by 4
13p 65 3 p
13 = 13 4 × 4 = 9 × 4
⇒ p = 5 3 p = 36
Hence, p = 5 is the solution of the Dividing both sides by 3
given equation. 3p 36
3 = 3

⇒ p = 12
Hence, p = 12 is the solution of the given equation.