What is the solution of |2w - 7| + 3 < 5

Answer 1

To solve the inequality \( |2w - 7| + 3 < 5 \), we first isolate the absolute value expression.

1. Subtract 3 from both sides: \[ |2w - 7| < 5 - 3 \] \[ |2w - 7| < 2 \]

2. Now, we can break the absolute value inequality into two separate inequalities: \[ -2 < 2w - 7 < 2 \]

3. We will solve these two inequalities separately.

Solving \( 2w - 7 < 2 \):

\[ 2w < 2 + 7 \] \[ 2w < 9 \] \[ w < \frac{9}{2} \] \[ w < 4.5 \]

Solving \( -2 < 2w - 7 \):

\[ -2 + 7 < 2w \] \[ 5 < 2w \] \[ \frac{5}{2} < w \] \[ 2.5 < w \]

4. Combining both inequalities, we find: \[ 2.5 < w < 4.5 \]

Therefore, the solution to the inequality \( |2w - 7| + 3 < 5 \) is: \[ \boxed{(2.5, 4.5)} \]