Question

Complete the following questions and show all of your work.

What are the solutions to the compound inequality 6c+8≤−10
or 8c+12>20
?

simple equations no explanation

Answer 1

To solve the compound inequality \( 6c + 8 \leq -10 \) or \( 8c + 12 > 20 \):

1. Solve \( 6c + 8 \leq -10 \):
\[
6c + 8 \leq -10
\]
Subtract 8 from both sides:
\[
6c \leq -10 - 8
\]
\[
6c \leq -18
\]
Divide by 6:
\[
c \leq -3
\]

2. Solve \( 8c + 12 > 20 \):
\[
8c + 12 > 20
\]
Subtract 12 from both sides:
\[
8c > 20 - 12
\]
\[
8c > 8
\]
Divide by 8:
\[
c > 1
\]

The solutions to the compound inequality \( 6c+8\leq−10 \) or \( 8c+12>20 \) are:
\[
c \leq -3 \quad \text{or} \quad c > 1
\]