Question

Solve the inequality and graph the solution. |2 x+9| \leq 15

Short answer

The solution to the inequality is -12 ≤ x ≤ 3

Step-by-step solution

Isolate the Absolute Value Expression

You'll first want to isolate the absolute value expression. In this case, the absolute value expression is already isolated on the left side of the inequality: \(|2x + 9| \leq 15\)

Solve for the Variable without the Absolute Value Sign

Remove the absolute value sign and solve for 'x' in the inequality, remembering that an absolute value inequality has two solutions: \(2x + 9 \leq 15\) and \(2x + 9 \geq -15\). Solving these gives \(x \leq 3\) and \(x \geq -12\), respectively.

Graph the Solutions

Now, plot the values of x on a number line. The solution set will be the overlap of both conditions, which in this case is -12 ≤ x ≤ 3.