Question

If LHS of an equation is $\frac{x-3}{2}$ and the solution of the equation is 6, then which of the following can be the RHS of this equation?

• A. $\frac{x}{4}$
• B. $\frac{x+6}{8}$
• C. $\frac{9}{x}$
• D. $\frac{3x}{2}$

Answer 1

Answer: (A), (B), (C)

The correct options are
A $\frac{x}{4}$
B $\frac{x+6}{8}$
C $\frac{9}{x}$

The solution of the equation is 6.
If we substitute $x=6$ in LHS we get,
$\frac{x-3}{2}=\frac{6-3}{2}=\frac{3}{2}$.

For the equation, the RHS should also be equal to $\frac{3}{2}$ when $x=6$.

Substituting $x=6$ in all the options, we get
$\left(i\right)\frac{x}{4}=\frac{6}{4}=\frac{3}{2}$

$\left(ii\right)\frac{x+6}{8}=\frac{6+6}{8}=\frac{12}{8}=\frac{3}{2}$

$\left(iii\right)\frac{9}{x}=\frac{9}{6}=\frac{3}{2}$

$\left(iv\right)\frac{3x}{2}=\frac{3\times 6}{2}=\frac{18}{2}=9$.

Hence, among all of the given options $\frac{x}{4}$, $\frac{x+6}{8}$ and $\frac{9}{x}$ can be the RHS of the equation.