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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 $ If $x \ge -7, 2x-1=x+7 \Rightarrow x=8$
If $x < -7, 2x -1 = -(x + 7)$
$\Rightarrow 3x=-6\Rightarrow x=-2$, which is not possible. .