Question
Solve the following equation and verify the answer: $6(1 - 4x) + 7(2 + 5x) = 53$
✓
Answer
$6(1 - 4 x) + 7(2 + 5x) - 53 $
$\Rightarrow 6 - 24x + 14 + 35x = 53$ (Removing brackets)
$\Rightarrow -24x + 35x + 14 + 6 = 53 $
$\Rightarrow 11x + 20 = 53 $
$\Rightarrow 11x = 53 - 20 $
$\Rightarrow 11x = 33$ (Transposing $20$ to $R.H.S.)$
$\Rightarrow\frac{\text{11x}}{11}=\frac{33}{11}$(Dividing both sides by $11)$
$\Rightarrow x = 3$
So, $x = 3$ is a solution of the given equation.
Check: Substituting $x = 3$ in the given equation,
we get, $L.H.S. = 6 (1 - 4 \times 3) + 7(2 + 5 \times 3)$
$= 6(1 - 12) + 7(2 + 15)$
$= 6 \times (-11) + 7 \times 17$
$= -66 + 119 = 53$
$= R.H.S.$
$\therefore$ When $x = 3,$
we have $L.H.S. = R.H.S.$
$\Rightarrow 6 - 24x + 14 + 35x = 53$ (Removing brackets)
$\Rightarrow -24x + 35x + 14 + 6 = 53 $
$\Rightarrow 11x + 20 = 53 $
$\Rightarrow 11x = 53 - 20 $
$\Rightarrow 11x = 33$ (Transposing $20$ to $R.H.S.)$
$\Rightarrow\frac{\text{11x}}{11}=\frac{33}{11}$(Dividing both sides by $11)$
$\Rightarrow x = 3$
So, $x = 3$ is a solution of the given equation.
Check: Substituting $x = 3$ in the given equation,
we get, $L.H.S. = 6 (1 - 4 \times 3) + 7(2 + 5 \times 3)$
$= 6(1 - 12) + 7(2 + 15)$
$= 6 \times (-11) + 7 \times 17$
$= -66 + 119 = 53$
$= R.H.S.$
$\therefore$ When $x = 3,$
we have $L.H.S. = R.H.S.$
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