Question

solve the following inequality algebraically. 3|x - 7| + 8 > 29

Explanation:

Step1: Isolate absolute value term

Subtract 8 from both sides:
$3|x - 7| + 8 - 8 > 29 - 8$
$3|x - 7| > 21$

Step2: Simplify the inequality

Divide both sides by 3:
$\frac{3|x - 7|}{3} > \frac{21}{3}$
$|x - 7| > 7$

Step3: Split absolute value inequality

For $|A| > B$, solve $A > B$ and $A < -B$:

1. $x - 7 > 7$
2. $x - 7 < -7$

Step4: Solve first linear inequality

Add 7 to both sides:
$x - 7 + 7 > 7 + 7$
$x > 14$

Step5: Solve second linear inequality

Add 7 to both sides:
$x - 7 + 7 < -7 + 7$
$x < 0$

Answer:

$x < 0$ or $x > 14$