Solve and write interval notation for the solution set. Then graph the solution set. \( x+14 \leq-\frac{1}{2} \) or \( x+14 \geq \frac{1}{2} \)

Solve the equation \( x+14 \leq-\frac{1}{2} \). Solve the inequality by following steps: - step0: Solve for \(x\): \(x+14\leq -\frac{1}{2}\) - step1: Move the constant to the right side: \(x\leq -\frac{1}{2}-14\) - step2: Subtract the numbers: \(x\leq -\frac{29}{2}\) Solve the equation \( x+14 \geq \frac{1}{2} \). Solve the inequality by following steps: - step0: Solve for \(x\): \(x+14\geq \frac{1}{2}\) - step1: Move the constant to the right side: \(x\geq \frac{1}{2}-14\) - step2: Subtract the numbers: \(x\geq -\frac{27}{2}\) The solution set for the given inequality is \( x \leq -\frac{29}{2} \) or \( x \geq -\frac{27}{2} \). To graph the solution set, we need to plot the points \( x = -\frac{29}{2} \) and \( x = -\frac{27}{2} \) on the number line and shade the regions that satisfy the inequality. The solution set is the union of the two intervals \( (-\infty, -\frac{29}{2}] \) and \( [-\frac{27}{2}, \infty) \).