Question

Solve the following equation and verify the answer:

\[\frac{3}{4} (x - 1) = x - 3\]

Answer 1

\[\frac{3}{4} (x - 1) = x - 3\]

\[\Rightarrow \frac{3}{4} \times x - \frac{3}{4} \times 1 = x - 3\] [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 `-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 sides:

\[L . H . S . : \frac{3}{4}\left( 9 - 1 \right) \]
\[ = \frac{3}{4}(8) \]
\[ = 6 \]
\[R . H . S . : 9 - 3 = 6\]

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