Solve and write interval notation for the solution set. Then graph the solution set. \[ 2 x+7 \leq-8 \text { or } 2 x+7 \geq 8 \] Select the correct choice below and fill in any answer boxes in your choice. A. The solution set is (Type your answer in interval notation. Use integers or fractions for any numbers in the expression.) B. There is no solution.

To solve the inequalities, let's break them down. 1. **First Inequality:** \[ 2x + 7 \leq -8 \] Subtract 7 from both sides: \[ 2x \leq -15 \] Now divide by 2: \[ x \leq -7.5 \] 2. **Second Inequality:** \[ 2x + 7 \geq 8 \] Subtract 7 from both sides: \[ 2x \geq 1 \] Now divide by 2: \[ x \geq 0.5 \] Putting it all together, the solution set in interval notation is: \[ (-\infty, -7.5] \cup [0.5, \infty) \] Now, for the graph, you would represent: - A shaded line from \(-\infty\) to \(-7.5\) with a closed circle at \(-7.5\). - Another shaded line starting from \(0.5\) to \(\infty\) with a closed circle at \(0.5\). Enjoy the versatility of intervals! They can be used to express everything from constraints in math problems to analyzing data ranges. Applying this knowledge, you can tackle needs in fields like economics and engineering where specifying ranges is essential. Don't forget, when solving inequalities, always pay attention to flipping the inequality sign when multiplying or dividing by a negative number! It's a common pitfall, so double-check your operations.