Question

solve the inequality. |2x + 5| < 9 select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the solution set is. (simplify your answer. type your answer in interval notation. use integers or fractions for any numbers in the expression.) b. the solution set is ∅.

Explanation:

Step1: Apply absolute value inequality rule

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

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: \(\frac{-14}{2} < \frac{2x}{2} < \frac{4}{2}\), resulting in \(-7 < x < 2\).

Answer:

A. The solution set is \((-7, 2)\)