Question

1. 3|2z - 4| - 6 > 12

Explanation:

Step1: Isolate the absolute value term

Add 6 to both sides of the inequality:
$3|2z - 4| - 6 + 6 > 12 + 6$
Simplify to get:
$3|2z - 4| > 18$

Step2: Divide by the coefficient of the absolute value

Divide both sides by 3:
$\frac{3|2z - 4|}{3} > \frac{18}{3}$
Simplify to get:
$|2z - 4| > 6$

Step3: Solve the compound inequality

The absolute value inequality $|2z - 4| > 6$ is equivalent to two separate inequalities:
$2z - 4 > 6$ or $2z - 4 < -6$

Sub - step 3.1: Solve $2z - 4 > 6$

Add 4 to both sides:
$2z - 4 + 4 > 6 + 4$
$2z > 10$
Divide both sides by 2:
$z > 5$

Sub - step 3.2: Solve $2z - 4 < -6$

Add 4 to both sides:
$2z - 4 + 4 < -6 + 4$
$2z < -2$
Divide both sides by 2:
$z < -1$

Answer:

The solution to the inequality is $z < - 1$ or $z > 5$