Question

If $\frac{1}{4}\left(10h\right)-\frac{3}{2}(h+1)=-\frac{2}{3}\left(\frac{9}{2}h\right)+6$, then the value of $h$ is:

• A. $\frac{9}{8}$
• B. $\frac{15}{8}$
• C. There is no value of $h$ for which the equation is true
• D. There are infinitely many values of $h$ for which the equation is true

Answer 1

The correct option is B $\frac{15}{8}$

Given, $\frac{1}{4}\left(10h\right)-\frac{3}{2}(h+1)=-\frac{2}{3}\left(\frac{9}{2}h\right)+6$

$\Rightarrow \frac{10h}{4}-\frac{3h}{2}-\frac{3}{2}=-3h+6$ ...[By Distribution Law]

$\Rightarrow \frac{10h-6h}{4}-\frac{3}{2}=-3h+6$ ...[Simplifying].

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

$\Rightarrow \frac{4h}{4}+3h=6+\frac{3}{2}$

$\Rightarrow \frac{4h+12h}{4}=\frac{12+3}{2}$

$\Rightarrow \frac{16h}{4}=\frac{15}{2}$

$\Rightarrow 4h=\frac{15}{2}$

$\Rightarrow h=\frac{15}{8}$.

Hence, option $B$ is correct.