Question

solve the inequality and graph the solution.
2 + 2c ≤ 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 2 from both sides

To isolate the term with \( c \), we subtract 2 from both sides of the inequality \( 2 + 2c \leq 10 \). This gives us \( 2 + 2c - 2 \leq 10 - 2 \), which simplifies to \( 2c \leq 8 \).

Step2: Divide by 2

Next, we divide both sides of the inequality \( 2c \leq 8 \) by 2 to solve for \( c \). This gives us \( \frac{2c}{2} \leq \frac{8}{2} \), which simplifies to \( c \leq 4 \).

To graph the solution:

• The endpoint is at \( c = 4 \). Since the inequality is \( \leq \), we use a closed dot at 4.
• Then we draw a ray to the left of 4 (towards negative infinity) to represent all values of \( c \) that are less than or equal to 4.

Answer:

The solution to the inequality \( 2 + 2c \leq 10 \) is \( c \leq 4 \). For the graph, place a closed dot at 4 on the number line and draw a ray extending to the left from 4.