Question
Solve the following equation and verify the answer: $3(2 - 5x) - 2(1 - 6x) = 1$
✓
Answer
$3(2 - 5x) - 2(1 - 6x) = 1$
$\Rightarrow 6 - 15x - 2 + 12x = 1$ (Removing brackets)
$\Rightarrow 6 - 2 - 15x + 12x = 1$
$\Rightarrow 4 - 3x$
$= 1 -3x = 1 - 4 ($Transposing $4$ to $R.H.S.)$
$\Rightarrow -3x = -3$
$\Rightarrow\frac{\text{-3x}}{-3}=\frac{-3}{-3}$
(Dividing both sides by $-3)$
$\Rightarrow x = 1$ So, $x = 1$ is a solution of the given equation.
Check: Substituting $x = 1$ in the given equation,
we get $L.H.S. = 3(2 - 5 \times 1) - 2(1- 6 \times 1)$
$=3(2 - 5) - 2(1 - 6)$
$=[3 \times (-3)] + [-2 \times (-5)]$
$= -9 + 10 = 1 = R.H.S.$
$\therefore$ When x = 1, we have $L.H.S. = R.H.S.$
$\Rightarrow 6 - 15x - 2 + 12x = 1$ (Removing brackets)
$\Rightarrow 6 - 2 - 15x + 12x = 1$
$\Rightarrow 4 - 3x$
$= 1 -3x = 1 - 4 ($Transposing $4$ to $R.H.S.)$
$\Rightarrow -3x = -3$
$\Rightarrow\frac{\text{-3x}}{-3}=\frac{-3}{-3}$
(Dividing both sides by $-3)$
$\Rightarrow x = 1$ So, $x = 1$ is a solution of the given equation.
Check: Substituting $x = 1$ in the given equation,
we get $L.H.S. = 3(2 - 5 \times 1) - 2(1- 6 \times 1)$
$=3(2 - 5) - 2(1 - 6)$
$=[3 \times (-3)] + [-2 \times (-5)]$
$= -9 + 10 = 1 = R.H.S.$
$\therefore$ When x = 1, we have $L.H.S. = R.H.S.$
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