Question

Solve each of the following equations and check your answers:
8(2x − 5) − 6(3x − 7) = 1

Answer 1

8(2x − 5) − 6(3x − 7) = 1
On expanding the brackets, we get
⇒ (8$\times$2x) $-$ (8 $\times$ 5) $-$ (6 $\times$ 3x) + ($-$6)$\times$($-$7) = 1
⇒ 16x $-$ 40 $-$ 18x + 42 = 1
⇒ 16x $-$ 18x + 42 $-$ 40 = 1
⇒ $-$2x + 2 = 1
Subtracting 2 from both sides, we get
⇒ $-$2x + 2 $-$ 2 = 1 $-$ 2
⇒ $-$2x = $-$1
Multiplying both sides by $-$1, we get
⇒ $-$2x $\times$($-$1) = $-$1$\times$($-$1)
⇒ 2x = 1
Dividing both sides by 2, we get
⇒ $\frac{2x}{2}=\frac{1}{2}$
⇒ x = $\frac{1}{2}$
Verification:
Substituting x = $\frac{1}{2}$ in LHS, we get
= 8(2$\times$$\frac{1}{2}$ $-$ 5) $-$ 6(3$\times$$\frac{1}{2}$ − 7)

= 8(1 − 5) − 6($\frac{3}{2}$ − 7)

= 8$\times$(−4) − (6 $\times$$\frac{3}{2}$) + (6 $\times$7)
= −32 − 9 + 42 = − 41 + 42 = 1 = RHS
LHS = RHS
Hence, verified.