Question

solve the inequality and graph the solution.
$\frac{p}{2} geq -4$
plot the endpoints. select an endpoint to change it from closed to open. select the middle of the segment, ray, or line to delete it.
submit

Explanation:

Step1: Multiply both sides by 2

To solve the inequality \(\frac{p}{2} \geq -4\), we multiply both sides by 2 to isolate \(p\). Multiplying both sides of an inequality by a positive number (in this case, 2) does not change the direction of the inequality sign. So we have:

$$ \frac{p}{2} \times 2 \geq -4 \times 2 $$

Step2: Simplify both sides

Simplifying the left side, \(\frac{p}{2} \times 2 = p\). Simplifying the right side, \(-4 \times 2 = -8\). So the solution to the inequality is:

$$ p \geq -8 $$

To graph the solution:

• The endpoint is at \(p = -8\). Since the inequality is \(\geq\), we use a closed circle at \(-8\) (because \(-8\) is included in the solution set).
• Then we draw a ray to the right of \(-8\) to represent all numbers greater than or equal to \(-8\).

Answer:

The solution to the inequality is \(p \geq -8\). For the graph, place a closed circle at \(-8\) on the number line and draw a ray extending to the right from \(-8\).