Find the solution to the equation
$5 (x - 3) - 7 (6 - x) = 24 - 3 (8 - x) - 3$

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Solution

$5 (x - 3) - 7 (6 - x) = 24 - 3 (8 - x) - 3$
Removing the brackets from both sides first and then simplifying:
$5 x - 15 - 42 + 7 x = 24 - 24 + 3 x - 3$
$\Rightarrow 5 x + 7 x - 15 - 42 = 3 x - 3$
$\Rightarrow 12 x - 57 = 3 x - 3$
Adding $57$ to both sides, we get
$12 x = 3 x - 3 + 57 = 3 x + 54$
Subtracting $3 x$ from both sides, we get
$12 x - 3 x = 54$
$\Rightarrow 9 x = 54$
$∴ x = \frac{54}{9} = 6$
$∴ x = 6$

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