Question

1. |2x + 1| - 4 < 5

Explanation:

Step1: Isolate the absolute value

Add 4 to both sides:
$$|2x + 1| < 5 + 4$$
$$|2x + 1| < 9$$

Step2: Rewrite without absolute value

For $|A| < b$, $-b < A < b$:
$$-9 < 2x + 1 < 9$$

Step3: Subtract 1 from all parts

$$-9 - 1 < 2x < 9 - 1$$
$$-10 < 2x < 8$$

Step4: Divide by 2

$$\frac{-10}{2} < x < \frac{8}{2}$$
$$-5 < x < 4$$

Answer:

$-5 < x < 4$