Solve for c.

Question

c+12
3
<3 or
3c+2
4
≥5
Write your answer as a compound inequality with integers.

Answer 1

To solve the compound inequality \( \frac{c + 12}{3} < 3 \) or \( \frac{3c + 2}{4} \geq 5 \), we will solve each inequality separately.

First Inequality: \(\frac{c + 12}{3} < 3\)

1. Multiply both sides by 3 to eliminate the fraction: \[ c + 12 < 9 \]
2. Subtract 12 from both sides: \[ c < 9 - 12 \] \[ c < -3 \]

Second Inequality: \(\frac{3c + 2}{4} \geq 5\)

1. Multiply both sides by 4 to eliminate the fraction: \[ 3c + 2 \geq 20 \]
2. Subtract 2 from both sides: \[ 3c \geq 20 - 2 \] \[ 3c \geq 18 \]
3. Divide both sides by 3: \[ c \geq 6 \]

Combine the Results

From the first inequality, we found \( c < -3 \).

From the second inequality, we found \( c \geq 6 \).

The solution can be expressed as a compound inequality: \[ c < -3 \quad \text{or} \quad c \geq 6 \]

Final Answer

Thus, the solution is: \[ c < -3 \quad \text{or} \quad c \geq 6 \]