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  4. Solution of 2x - 1 = | x + 7| is

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Q. Solution of $2x - 1 = | x + 7|$ is

Linear Inequalities

Solution:

$2x - 1 = |x + 7| $ $ = \begin{cases} x + 7 ,& \text{if $x \ge -7$ } \\[2ex] -(x + 7) ,& \text{if $x < -7$ } \end{cases}$
$ \therefore \quad$ If $x \ge - 7$, $2 x - 1 = x + 7 \Rightarrow x= 8$
If $x < - 7$, $2x - 1 = - \left(x + 7\right) \Rightarrow 3x = - 6$
$\Rightarrow \quad x = - 2$, Not possible.