Question

hand in on seperate shect of paper
① |x + 4| + 3 = 17
② |3x + 4| = -3
③ |3z| - 4 > 8
④ |3x - 6| + 3 < 15
new section tomorrow

Explanation:

Step1: Isolate absolute value term

$|x+4| = 17 - 3$
$|x+4| = 14$

Step2: Solve for positive case

$x+4 = 14$
$x = 14 - 4$
$x = 10$

Step3: Solve for negative case

$x+4 = -14$
$x = -14 - 4$
$x = -18$

---

Step1: Analyze absolute value property

An absolute value cannot equal a negative number, so there is no solution.

---

Step1: Isolate absolute value term

$|3z| > 8 + 4$
$|3z| > 12$

Step2: Rewrite as compound inequality

$3z > 12$ or $3z < -12$

Step3: Solve each inequality

$z > \frac{12}{3} = 4$ or $z < \frac{-12}{3} = -4$

---

Step1: Isolate absolute value term

$|3x-6| < 15 - 3$
$|3x-6| < 12$

Step2: Rewrite as compound inequality

$-12 < 3x-6 < 12$

Step3: Add 6 to all parts

$-12 + 6 < 3x < 12 + 6$
$-6 < 3x < 18$

Step4: Divide by 3

$\frac{-6}{3} < x < \frac{18}{3}$
$-2 < x < 6$

Answer:

1. $x = 10$ or $x = -18$
2. No solution
3. $z > 4$ or $z < -4$
4. $-2 < x < 6$