Solve and write interval notation for the solution set. Then graph the solution set. \[ 2 x+5 \leq-6 \text { or } 2 x+5 \geq 6 \]

To solve the compound inequality \( 2x + 5 \leq -6 \) or \( 2x + 5 \geq 6 \), we will solve each inequality separately. ### Step 1: Solve the first inequality 1. Start with the inequality: \[ 2x + 5 \leq -6 \] 2. Subtract 5 from both sides: \[ 2x \leq -6 - 5 \] \[ 2x \leq -11 \] 3. Divide both sides by 2: \[ x \leq -\frac{11}{2} \] ### Step 2: Solve the second inequality 1. Start with the inequality: \[ 2x + 5 \geq 6 \] 2. Subtract 5 from both sides: \[ 2x \geq 6 - 5 \] \[ 2x \geq 1 \] 3. Divide both sides by 2: \[ x \geq \frac{1}{2} \] ### Step 3: Combine the solutions The solution set consists of two parts: - From the first inequality: \( x \leq -\frac{11}{2} \) - From the second inequality: \( x \geq \frac{1}{2} \) ### Step 4: Write in interval notation The solution set in interval notation is: \[ (-\infty, -\frac{11}{2}] \cup [\frac{1}{2}, \infty) \] ### Step 5: Graph the solution set To graph the solution set, we will represent the intervals on a number line. 1. Draw a number line. 2. Shade the region to the left of \(-\frac{11}{2}\) and include the endpoint (closed circle). 3. Shade the region to the right of \(\frac{1}{2}\) and include the endpoint (closed circle). Now, let's graph the solution set. ### Graphing the solution set The graph will show two shaded regions, one extending to the left from \(-\frac{11}{2}\) and the other extending to the right from \(\frac{1}{2}\). I will now provide the graph. (Note: As a text-based AI, I cannot create visual graphs directly, but you can visualize it based on the description above.)