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

Explanation:

Step1: Isolate the absolute - value term

Subtract 8 from both sides of the inequality $3|x - 7|+8>29$. $3|x - 7|+8 - 8>29 - 8$ $3|x - 7|>21$

Step2: Further isolate the absolute - value

Divide both sides of the inequality $3|x - 7|>21$ by 3. $\frac{3|x - 7|}{3}>\frac{21}{3}$ $|x - 7|>7$

Step3: Consider two cases

Case 1: $x-7>7$ Add 7 to both sides: $x-7 + 7>7 + 7$, so $x>14$. Case 2: $x - 7<-7$ Add 7 to both sides: $x-7 + 7<-7 + 7$, so $x<0$.

Answer:

$x<0$ or $x>14$