Question

Solve each of the following equations and verify the answer in each case:
6(1 − 4x) + 7(2 + 5x) = 53

Answer 1

6(1 − 4x) + 7(2 + 5x) = 53
or, $6\times 1-6\times 4x+7\times 2+7\times 5x=53$ [On expanding the brackets]
or, 6 $-$ 24x + 14 + 35x = 53
or, 11x + 20 = 53
or, 11x + 20 $-$ 20 = 53 $-$ 20 [Subtracting 20 from both the sides]
or, 11x = 33
or, $\frac{11x}{11}=\frac{33}{11}$ [Dividing both the sides by 11]
or, x = 3
Verification:
Substituting x = 3 in the L.H.S.:
$$\begin{gathered} 6(1-4\times 3)+7(2+5\times 3) \\ \Rightarrow 6(1-12)+7(2+15) \\ \Rightarrow 6(-11)+7\left(17\right) \\ \Rightarrow -66+119=53=R.H.S. \end{gathered}$$

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