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
6
𝑐
+
8
≤
−
10
or 8c+12>20
8
𝑐
+
12
>
20
?



HINT : Compound Inequalties

Answer 1

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

### Solving the first inequality: \( 6c + 8 \leq -10 \)

1. Start with the inequality:
\[
6c + 8 \leq -10
\]

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

3. Divide both sides by 6:
\[
c \leq -3
\]

### Solving the second inequality: \( 8c + 12 > 20 \)

1. Start with the inequality:
\[
8c + 12 > 20
\]

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

3. Divide both sides by 8:
\[
c > 1
\]

### Combining the solutions:
The solutions to the compound inequality are:
- For the first part: \( c \leq -3 \)
- For the second part: \( c > 1 \)

### Final answer:
The solutions are:
\[
c \leq -3 \quad \text{or} \quad c > 1
\]

This means that any value of \( c \) that is less than or equal to -3, or greater than 1, satisfies the compound inequality.