Question

Solve each of the following equations and verify the answer in each case:
$\frac{3}{4}(x-1)=x-3$

Answer 1

$\frac{3}{4}\left(x-1\right)=x-3$
$\Rightarrow \frac{3}{4}\times x-\frac{3}{4}\times 1=x-3$ [On expanding the brackets]
$\Rightarrow \frac{3x}{4}-\frac{3}{4}=x-3$
$\Rightarrow \frac{3x}{4}-x=-3+\frac{3}{4}$ [Transposing x to the L.H.S. and $-\frac{3}{4}$ to the R.H.S.]
$\Rightarrow \frac{3x-4x}{4}=\frac{-12+3}{4}$
$\Rightarrow \frac{-x}{4}=\frac{-9}{4}$
$\Rightarrow \frac{-x}{4}\times \left(-4\right)=\frac{-9}{4}\times \left(-4\right)$ [Multiplying both the sides by -4]
or, x = 9

Verification:
Substituting x = 9 on both the sides:
$$\begin{gathered} L.H.S.:\frac{3}{4}\left(9-1\right) \\ =\frac{3}{4}\left(8\right) \\ =6 \\ R.H.S.:9-3=6 \end{gathered}$$

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