Question

solve the inequality and graph the solution. 5 + 2c ≤ -7 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. <----|----|----|----|----|----|----|----|----|----|----> -10 -8 -6 -4 -2 0 2 4 6 8 10 submit

Explanation:

Step1: Subtract 5 from both sides

To isolate the term with \( c \), we subtract 5 from both sides of the inequality \( 5 + 2c \leq -7 \).
\[
5 + 2c - 5 \leq -7 - 5
\]
Simplifying both sides, we get:
\[
2c \leq -12
\]

Step2: Divide by 2

To solve for \( c \), we divide both sides of the inequality \( 2c \leq -12 \) by 2.
\[
\frac{2c}{2} \leq \frac{-12}{2}
\]
Simplifying both sides, we find:
\[
c \leq -6
\]

Answer:

The solution to the inequality \( 5 + 2c \leq -7 \) is \( c \leq -6 \). To graph this, we plot a closed dot at \( -6 \) (since the inequality is "less than or equal to") and draw a ray to the left of \( -6 \) on the number line.