Question

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

solution(s):________

Explanation:

Step1: Isolate the absolute value

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.
$-\frac{3}{2} - 1 < x < \frac{3}{2} - 1$
Simplify constants: $-\frac{3}{2}-\frac{2}{2}=-\frac{5}{2}$, $\frac{3}{2}-\frac{2}{2}=\frac{1}{2}$

Answer:

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