Page 151 - ICSE Math 7

Example 4: Solve 5p + 2 = 17 by trial and error method. Try This
Solution: 5p + 2 = 17
(i) Putting p = 1, LHS = 5(1) + 2 = 7 ≠ 17 Solve the following by trial and
 LHS ≠ RHS, ∴ p = 1 is not the solution. error method.
(a) 3p –2 = 7
(ii) Putting p = 2, LHS = 5(2) + 2 = 12 ≠ 17 (b) 2m + 3 = 5
 LHS ≠ RHS, ∴ p = 2 is not the solution. (c) x + 5 = 4
(iii) Putting p = 3, LHS = 5(3) + 2 = 17 = RHS
 LHS = RHS, ∴ p = 3 is the solution.

Rules for Solving an Equation

To solve an equation keep in mind the following rules:
Rule 1: If we add or subtract the same number on both sides of the equation, it still holds true,
i.e., equation is not affected in any way.
Rule 2: If we multiply or divide both sides of the equation by the same non-zero number, it still
holds true, i.e., the equation is not affected in any way.
Let’s learn it with an example.
2x + 3 = 7 ⇒ 2x + 3 – 3 = 7 – 3 ⇒ 2x = 4

x x x x x x

4
⇒ 2x = ⇒ x = 2
2 2

x

The rules mentioned above are helpful in balancing and solving linear equations.
Example 5: Solve the following equations.
a
(a) 6m = 18 (b) 3n – 2 = 25 (c) 20p = 40 (d) = 9
3 5 15
Solution: (a) 6m = 18 (b) 3n – 2 = 25
Divide both sides by 6 Add 2 to both sides
⇒ 6m = 18 ⇒ m = 3 ⇒ 3n – 2 + 2 = 25 + 2 ⇒ 3n = 27
6 6
Divide both sides by 3

(c) 20p = 40 ⇒ 3n = 27 ⇒ n = 9
3 3 3
9
Multiply both sides by 3 (d) a = 15
5
⇒ 20p × 3 = 40 × 3 Multiply both sides by 5
3
a
⇒ 20p = 120 ⇒ × 5 = 9 × 5 ⇒ a = 3
5 15
Divide both sides by 20
20p 120
⇒ = ⇒ p = 6
20 20

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