Question

1. $2|x+1|<3$

solutio

Explanation:

Step1: Isolate absolute value term

Divide both sides by 2:
$\frac{2|x+1|}{2} < \frac{3}{2}$
Simplify to get:
$|x+1| < \frac{3}{2}$

Step2: Rewrite without absolute value

For $|A| < b$, $-b < A < b$:
$-\frac{3}{2} < x+1 < \frac{3}{2}$

Step3: Solve for x

Subtract 1 from all parts:
$-\frac{3}{2} - 1 < x < \frac{3}{2} - 1$
Convert 1 to $\frac{2}{2}$ for common denominators:
$-\frac{3}{2} - \frac{2}{2} < x < \frac{3}{2} - \frac{2}{2}$
Simplify each term:
$-\frac{5}{2} < x < \frac{1}{2}$

Answer:

$-\frac{5}{2} < x < \frac{1}{2}$