Solve for q.

Question

5–6q≥
–
16q–15≥
–
6q–15
Write your answer as a compound inequality with integers.

Answer 1

To solve the compound inequality \( 5 - 6q \geq -16q - 15 \) and \( -16q - 15 \geq -6q - 15 \), we will solve each part separately.

First Inequality

1. Start with the first inequality: \[ 5 - 6q \geq -16q - 15 \]

2. Add \( 16q \) to both sides: \[ 5 + 10q \geq -15 \]

3. Subtract 5 from both sides: \[ 10q \geq -20 \]

4. Divide by 10: \[ q \geq -2 \]

Second Inequality

1. Now for the second inequality: \[ -16q - 15 \geq -6q - 15 \]

2. Add \( 15 \) to both sides: \[ -16q \geq -6q \]

3. Add \( 16q \) to both sides: \[ 0 \geq 10q \]

4. Divide by 10 (note that we reverse the inequality since we divide by a negative number): \[ 0 \leq q \]

   or equivalently: \[ q \leq 0 \]

Combined Results

Now we combine the results of both inequalities: \[ -2 \leq q \leq 0 \]

Thus, the solution can be written as the compound inequality: \[ \boxed{-2 \leq q \leq 0} \]