Page 116 - Start Up Mathematics_7

Example 8: Write the step you will use to separate the variable and then solve the equation:
x 5 a 9
(a) 6m = 18 (b) 5x = –20 (c) = (d) =
3 6 5 15

Solution: (a) 6m = 18 (b) 5x = –20

Divide both sides by 6 Divide both sides by 5
6m 18 5x –20
⇒ = ⇒ =
6 6 5 5
⇒ m = 3 ⇒ x = –20 = –4

x 5 5
a
(c) = (d) = 9
3 6 5 15
Multiply both sides by 3 Multiply both sides by 5
x 5 a 9
⇒ × 3 = × 3 ⇒ × 5 = × 5
3 6 5 15
5
⇒ x = ⇒ a = 3
2

Example 9: Write the step(s) you will use to separate the variable and then solve the equation:
20p
(a) 3n – 2 = 25 (b) = 40
3
Solution: (a) 3n – 2 = 25 (b) 20p = 40
3
Add 2 to both sides Multiply both sides by 3
⇒ 3n – 2 + 2 = 25 + 2 20p

⇒ 3n = 27 ⇒ 3 = 40 × 3
Divide both sides by 3 ⇒ 20p = 120
3n 27 Divide both sides by 20
⇒ =
3 3 20p 120
⇒ n = 9 ⇒ 20 = 20
⇒ p = 6
Example 10: Solve the following equations:
–p
(a) 7m = 49 (b) = 2 (c) 4r = 0 (d) 3q – 6 = 0
3
Solution: (a) 7m = 49 (b) –p = 2
7m 49 3
⇒ 7 = 7 ⇒ –p × 3 = 2 × 3

⇒ m = 7 3
⇒ p = –6

(c) 4r = 0 (d) 3q – 6 = 0
4r 0 ⇒ 3q – 6 + 6 = 0 + 6
⇒ =
4 4 ⇒ 3q = 6
⇒ r = 0 3q 6
⇒ 3 = 3
⇒ q = 2

108