Question

Solve each of the following equations and verify the answer in each case:
3(x + 6) + 2(x + 3) = 64

Answer 1

3(x + 6) + 2(x + 3) = 64
$\Rightarrow$3 × x + 3 × 6 + 2 × x + 2 × 3 = 64 [On expanding the brackets]
$\Rightarrow$3x + 18 + 2x + 6 = 64
⇒5x + 24 = 64
⇒5x + 24 $-$ 24 = 64 $-$ 24 [Subtracting 24 from both the sides]
⇒5x = 40
⇒$\frac{5x}{5}=\frac{40}{5}$ [Dividing both the sides by 5]
⇒x = 8
Verification:
Substituting x = 8 in the L.H.S.:
$$\begin{gathered} 3(8+6)+2(8+3) \\ 3\left(14\right)+2\left(11\right) \\ 42+22=64=R.H.S. \end{gathered}$$

L.H.S. = R.H.S.
Hence, verified.