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Method of Intervals

Solve for x...

Question

Solve for $x$ : $(x - 1) (x + 6) - (x - 2) (x - 3) = 3$

2 \frac{6}{7}

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2 \frac{1}{5}

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1 \frac{1}{2}

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1 \frac{3}{8}

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Solution

The correct option is C $1 \frac{1}{2}$
Given, $(x - 1) (x + 6) - (x - 2) (x - 3) = 3$
$\Rightarrow x (x + 6) - 1 (x + 6) - [x (x - 3) - 2 (x - 3)] = 3$
$\Rightarrow x^{2} + 6 x - x - 6 - (x^{2} - 3 x - 2 x + 6) = 3$
$\Rightarrow 5 x + 5 x - 6 - 6 = 3$
$\Rightarrow 10 x = 3 + 12$
$\Rightarrow 10 x = 15$
$\Rightarrow x = \frac{3}{2} = 1 \frac{1}{2}$

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