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