Question

solve the inequality and graph the solution.
2p + 6 ≥ -2
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.
-5 -4 -3 -2 -1 0 1 2 3 4 5
submit

Explanation:

Step1: Subtract 6 from both sides

To isolate the term with \( p \), we subtract 6 from both sides of the inequality \( 2p + 6 \geq -2 \). This gives us \( 2p + 6 - 6 \geq -2 - 6 \), which simplifies to \( 2p \geq -8 \).

Step2: Divide both sides by 2

To solve for \( p \), we divide both sides of the inequality \( 2p \geq -8 \) by 2. This gives us \( \frac{2p}{2} \geq \frac{-8}{2} \), which simplifies to \( p \geq -4 \).

Answer:

The solution to the inequality \( 2p + 6 \geq -2 \) is \( p \geq -4 \). To graph this, we plot a closed circle at \( -4 \) (since the inequality is "greater than or equal to") and draw a ray to the right from \( -4 \) on the number line.