Question

solve the inequality and graph the solution.
8 + 9c ≤ -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.
-5 -4 -3 -2 -1 0 1 2 3 4 5
submit

Explanation:

Step1: Subtract 8 from both sides

To isolate the term with \( c \), we subtract 8 from both sides of the inequality \( 8 + 9c \leq -10 \). This gives us \( 8 + 9c - 8 \leq -10 - 8 \), which simplifies to \( 9c \leq -18 \).

Step2: Divide by 9

Next, we divide both sides of the inequality \( 9c \leq -18 \) by 9. Since 9 is a positive number, the direction of the inequality sign remains the same. So, \( \frac{9c}{9} \leq \frac{-18}{9} \), which simplifies to \( c \leq -2 \).

To graph this solution:

• The endpoint is at \( c = -2 \). Since the inequality is \( \leq \), we use a closed dot at \( -2 \).
• Then, we draw a ray to the left of \( -2 \) (towards negative infinity) to represent all values of \( c \) that are less than or equal to \( -2 \).

Answer:

The solution to the inequality \( 8 + 9c \leq -10 \) is \( c \leq -2 \). For the graph, place a closed dot at \( -2 \) and draw a ray extending to the left from \( -2 \).