Question

solve the following inequality algebraically.
2|x - 5|+7 < 11

Explanation:

Step1: Isolate the absolute - value term

Subtract 7 from both sides of the inequality:
$2|x - 5|+7-7<11 - 7$
$2|x - 5|<4$

Step2: Further isolate the absolute - value term

Divide both sides of the inequality by 2:
$\frac{2|x - 5|}{2}<\frac{4}{2}$
$|x - 5|<2$

Step3: Rewrite the absolute - value inequality

If $|u|0$), then $-a < u < a$. Here $u=x - 5$ and $a = 2$. So we have:
$-2

Step4: Solve for x

Add 5 to all parts of the compound inequality:
$-2+5$3

Answer:

$3