Question

Tick (✓) the correct answer
If (2^{3x − 1} + 10) ÷ 7 = 6, then x is equal to
(a) −2
(b) 0
(c) 1
(d) 2

Answer 1

(d) 2

$$\begin{gathered} \left(2^{3x-1}+10\right)÷7=6 \\ \Rightarrow \frac{\left(2^{3x-1}+10\right)}{7}=\frac{6}{1} \\ \mathrm{On}\mathrm{cross}\mathrm{multiplying}: \\ \left(2^{3x-1}+10\right)\times 1=6\times 7=42 \end{gathered}$$

⇒ 2^3x-1 = 42 -10
⇒2^3x-1 = 32
⇒ 2^3x-1 = 2⁵
⇒ 3x-1 = 5
⇒ 3x = 6
Therefore, x = 2