Question

solve: |2x + 5| < 9. state the solution set as an interval and graph the solution set. enter solutions as integers or reduced fractions. if there is no solution, type dne in the answer box and leave the graph blank.
a. the solution set as an interval is:

b. the graph of the solution set is:

12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12
clear all draw:

Explanation:

Step1: Recall absolute value inequality rule

For \(|a| < b\) (where \(b>0\)), it is equivalent to \(-b < a < b\). So for \(|2x + 5| < 9\), we have \(-9 < 2x + 5 < 9\).

Step2: Subtract 5 from all parts

Subtract 5 from each part of the compound inequality: \(-9 - 5 < 2x + 5 - 5 < 9 - 5\), which simplifies to \(-14 < 2x < 4\).

Step3: Divide by 2

Divide each part by 2: \(\frac{-14}{2} < \frac{2x}{2} < \frac{4}{2}\), so \(-7 < x < 2\).

Answer:

A. The solution set as an interval is: \((-7, 2)\)

For part B (graphing), we would draw an open circle at \(-7\) and an open circle at \(2\) on the number line, then shade the region between them. But since the question asks to enter the interval for part A here, the interval is \((-7, 2)\).