Question

Solve each of the following equations and check your answers:
5(2 − 3x) − 17(2x − 5) = 16

Answer 1

5(2 − 3x) − 17(2x − 5) = 16
On expanding the brackets, we get
⇒ (5$\times$2) $-$ (5 $\times$ 3x) − (17 $\times$2x ) + (17$\times$5) = 16
⇒ 10 $-$ 15x − 34x + 85 = 16
⇒ 10 + 85 − 34x $-$ 15x = 16
⇒ 95 - 49x = 16
Subtracting 95 from both sides, we get
⇒ - 49x + 95 $-$ 95 = 16 $-$ 95
⇒ - 49x = -79
Dividing both sides by -49, we get
⇒ $\frac{-49x}{-49}=\frac{-79}{-49}$

⇒ x = $\frac{79}{49}$
Verification:
Substituting x = $\frac{79}{49}$ in LHS, we get
= 5(2 − 3$\times$$\frac{79}{49}$) − 17(2$\times$$\frac{79}{49}$ − 5)
= (5$\times$2) $-$ (5 $\times$ 3$\times$$\frac{79}{49}$ ) − (17 $\times$2$\times$$\frac{79}{49}$ ) + (17$\times$5)
= 10 $-$ $\frac{1185}{49}$ − $\frac{2686}{49}$ + 85
= $\frac{490-1185-2686+4165}{49}$
= $\frac{784}{49}$
= 16
= RHS
So, LHS = RHS
Hence, verified.