Question
Solve the following equation and verify the answer:
$\frac{\text{x-3}}{5}=-2=\frac{\text{2x}}{5}$

Answer

$\frac{\text{x-3}}{5}=-2=\frac{\text{2x}}{5}$ multiplying each term by 5, we get $\frac{(\text{x}-3)\times5}{5}-(2\times5)=\frac{\text{2x}}{5}\times5$ ⇒ x - 3 - 10 = 2x ⇒ x - 13 = 2x ⇒ x - 2x = 13 (Transposing 2x to L.H.S. and -13 to R.H.S.) ⇒ -x = 13 ⇒ x = -13 (Multiplying both sides by -1) So, x = -13 is a solution of the given equation. Check: Substituting x = -13 in the given equation, we get $\text{L.H.S.}=\frac{-13-3}{5}-2=\frac{-16}{5}-2$$=\frac{-16-10}{5}=\frac{-26}{5}$
$\text{R.H.S.}=\frac{2\times(-13)}{5}=\frac{-26}{5}$ $\therefore$ When x = -13, we have L.H.S. = R.H.S.

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