Question

Solve each of the following equations and check your answers:
6(1 − 4x) + 7(2 + 5x) = 53

Answer 1

6(1 − 4x) + 7(2 + 5x) = 53
On expanding the brackets, we get
⇒ (6$\times$1) $-$ (6 $\times$ 4x) + (7 $\times$2) + (7$\times$5x) = 53
⇒ 6 $-$ 24x + 14 + 35x = 53
⇒ 6 + 14 + 35x $-$ 24x = 53
⇒ 20 + 11x = 53
Subtracting 20 from both sides, we get
⇒ 20 + 11x $-$ 20 = 53 $-$ 20
⇒ 11x = 33
⇒ Dividing both sides by 11, we get
⇒ $\frac{11x}{11}=\frac{33}{11}$
⇒ x = 3

Verification:
Substituting x = 3 in LHS, we get
= 6(1 − 4$\times$3) + 7(2 + 5$\times$3)
= 6(1 − 12) + 7(2 + 15)
= 6(−11) + 7(17)
= −66 + 119 = 53 = RHS
LHS = RHS
Hence, verified.