Simplify: $7 - 9 [x - 5 (x + 2)] = 25 - 9 [x - 3 (8 - x)]$ .

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Solution

The correct option is A $2$
Given, $7 - 9 [x - 5 (x + 2)] = 25 - 9 [x - 3 (8 - x)]$ .

Simplifying both sides separately, we get:

LHS $= 7 - 9 [x - 5 (x + 2)]$
$= 7 - 9 x + 45 (x + 2)$ ...[By Distribution Law]
$= 7 - 9 x + 45 x + 90$ ...[By Distribution Law]
$= 36 x + 97$ .

RHS $= 25 - 9 [x - 3 (8 - x)]$
$= 25 - 9 x + 27 (8 - x)$ ...[By Distribution Law]
$= 25 - 9 x + 216 - 27 x$ ...[By Distribution Law]
$= 241 - 36 x$ .

Now, $L H S = R H S$
$⟹ 36 x + 97 = 241 - 36 x$ .

Transposing $x$ terms to one side, we get,
$⟹ 36 x + 36 x = 241 - 97$
$⟹ 72 x = 144$
$⟹ x = 2$ .

Hence, option $A$ is correct.

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