Question

Complete the following questions and show all of your work. , workout on paper and upload

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



HINT : Compound Inequalties

Answer 1

To solve the compound inequality \( 6c + 8 \leq -10 \) or \( 8c + 12 > 20 \), we will address each inequality separately.

### Step 1: Solve the first inequality \( 6c + 8 \leq -10 \)

1. Subtract 8 from both sides:
\[
6c \leq -10 - 8
\]
\[
6c \leq -18
\]

2. Divide both sides by 6:
\[
c \leq \frac{-18}{6}
\]
\[
c \leq -3
\]

### Step 2: Solve the second inequality \( 8c + 12 > 20 \)

1. Subtract 12 from both sides:
\[
8c > 20 - 12
\]
\[
8c > 8
\]

2. Divide both sides by 8:
\[
c > \frac{8}{8}
\]
\[
c > 1
\]

### Step 3: Combine the solutions

The solutions to the compound inequality are:
\[
c \leq -3 \quad \text{or} \quad c > 1
\]

### Final Answer

The solution set is:
\[
(-\infty, -3] \cup (1, \infty)
\]

This indicates that \( c \) can take any value less than or equal to -3 or greater than 1.