Question
Solve the following equation and verify the answer:
$\frac{3}{4}(\text{x}-1)=\text{x}-3$
$\frac{3}{4}(\text{x}-1)=\text{x}-3$
✓
Answer
$\frac{3}{4}(\text{x}-1)=\text{x}-3$ $\Rightarrow\frac{3}{4}(\text{x}-1)\times4=(\text{x}-3)\times4$ (Multiplying both sides by 4) ⇒ 3(x - 1) = 4(x - 3) ⇒ 3x - 3 = 4x - 12 (Removing brackets) ⇒ 3x - 4x = -12 + 3 (Transposing 4x to L.H.S. and -3 to R.H.S.) ⇒ -x = -9 ⇒ x = 9 So, x = 9 is a solution of the given equation. Check: Substituting x = 9 in the given equation, we get $\text{L.H.S}=\frac{3}{4}(9-1)=\frac{3}{4}\times8=6$$\text{R.H.S.}= 9 - 3 = 6$
$\therefore$ When x = 9, we have L.H.S. = R.H.S.
$\therefore$ When x = 9, we have L.H.S. = R.H.S.
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