Question

solve the inequality and graph the solution.
5h + 10 > -10
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.
(number line with ticks at -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5)

Explanation:

Step1: Subtract 10 from both sides

To isolate the term with \( h \), we subtract 10 from both sides of the inequality \( 5h + 10 > -10 \). This gives us \( 5h + 10 - 10 > -10 - 10 \), which simplifies to \( 5h > -20 \).

Step2: Divide both sides by 5

To solve for \( h \), we divide both sides of the inequality \( 5h > -20 \) by 5. This gives us \( \frac{5h}{5} > \frac{-20}{5} \), which simplifies to \( h > -4 \).

For graphing the solution:

• The endpoint is at \( h = -4 \). Since the inequality is \( h > -4 \) (not \( h \geq -4 \)), we use an open circle at \( -4 \) on the number line.
• Then we draw a ray to the right of \( -4 \) to represent all values of \( h \) that are greater than \( -4 \).

Answer:

The solution to the inequality \( 5h + 10 > -10 \) is \( h > -4 \). The graph has an open circle at \( -4 \) and a ray pointing to the right.