Question
Solve the following equation and verify the answer: $5(x - 1) + 2(x + 3) + 6 = 0$
✓
Answer
$5(x - 1) + 2(x + 3) + 6 = 0$
$\Rightarrow 5(x - 1) + 2(x + 3) = -6$ (Transposing $6$ to $R.H.S.)$
$\Rightarrow 5x - 5 + 2x + 6 = -6$ (Removing brackets)
$\Rightarrow 5x + 2x - 5 + 6 = -6$
$\Rightarrow 7x + 1 = -6$
$\Rightarrow 7x = -6 - 1$ (Transposing $1$ to $R.H.S.)$
$\Rightarrow 7x = -7$
$\Rightarrow\frac{\text{7x}}{7}=\frac{-7}{7}$(Dividing both sides by $7)$
$\Rightarrow x = -1$
So, $x = -1$ is a solution of the given equation.
Check: Substituting $x = -1$ in the given equation,
we get $L.H.S. = 5(-1 - 1) + 2(-1 + 3) + 6$
$= 5 \times (-2) + 2 \times 2 + 6 = 10+ 4 +6$
$= -10 + 10 = 0 = R.H.S$
$\therefore$When $x = -1$, we have
$L.H.S. = R.H.S.$
$\Rightarrow 5(x - 1) + 2(x + 3) = -6$ (Transposing $6$ to $R.H.S.)$
$\Rightarrow 5x - 5 + 2x + 6 = -6$ (Removing brackets)
$\Rightarrow 5x + 2x - 5 + 6 = -6$
$\Rightarrow 7x + 1 = -6$
$\Rightarrow 7x = -6 - 1$ (Transposing $1$ to $R.H.S.)$
$\Rightarrow 7x = -7$
$\Rightarrow\frac{\text{7x}}{7}=\frac{-7}{7}$(Dividing both sides by $7)$
$\Rightarrow x = -1$
So, $x = -1$ is a solution of the given equation.
Check: Substituting $x = -1$ in the given equation,
we get $L.H.S. = 5(-1 - 1) + 2(-1 + 3) + 6$
$= 5 \times (-2) + 2 \times 2 + 6 = 10+ 4 +6$
$= -10 + 10 = 0 = R.H.S$
$\therefore$When $x = -1$, we have
$L.H.S. = R.H.S.$
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