Question

solve the inequality and graph the solution. 8 + 5c < -10. use the endpoints. select an endpoint to change it from closed to open. select the middle of the segment, ray, or line to delete it.

Explanation:

Step1: Subtract 8 from both sides

To isolate the term with \( c \), we subtract 8 from both sides of the inequality \( 8 + 5c < -10 \). This gives us \( 8 + 5c - 8 < -10 - 8 \), which simplifies to \( 5c < -18 \).

Step2: Divide both sides by 5

Next, we divide both sides of the inequality \( 5c < -18 \) by 5 to solve for \( c \). This results in \( c < \frac{-18}{5} \), or \( c < -3.6 \).

Answer:

The solution to the inequality \( 8 + 5c < -10 \) is \( c < -3.6 \) (or \( c < \frac{-18}{5} \)). To graph this, we draw an open circle at \( -3.6 \) on the number line and shade the region to the left of \( -3.6 \).