Question

Find the value of $z$ in the given equation:
$\frac{z}{6}\left(\frac{3}{2}\right)-7=-2(3z-4)$.

• A. $-\frac{12}{5}$
• B. $-\frac{4}{25}$
• C. $\frac{4}{25}$
• D. $\frac{12}{5}$

Answer 1

The correct option is D $\frac{12}{5}$

Given, $\frac{z}{6}\left(\frac{3}{2}\right)-7=-2(3z-4)$

$\Rightarrow \frac{3z}{12}-7=-6z+8$ ...[By Distribution Law].

Transposing $x$ terms to one side, we get,

$\Rightarrow \frac{3z}{12}+6z=8+7$

$\Rightarrow \frac{3z+72z}{12}=15$ …[Cross-multiplying the denominators on the LHS]

$\Rightarrow \frac{75z}{12}=15$ ...[Simplifying]

$\Rightarrow z=\frac{12\times 15}{75}=\frac{12}{5}$.

Hence, option $D$ is correct.