Solve for w.

Question

3w+2≥8 or
3w+7
2
<5
Write your answer as a compound inequality with integers.

Answer 1

Let's solve each inequality separately.

1. For the first inequality: \[ 3w + 2 \geq 8 \] Subtract 2 from both sides: \[ 3w \geq 6 \] Divide both sides by 3: \[ w \geq 2 \]

2. For the second inequality: \[ \frac{3w + 7}{2} < 5 \] Multiply both sides by 2 (since 2 is positive, the inequality sign stays the same): \[ 3w + 7 < 10 \] Subtract 7 from both sides: \[ 3w < 3 \] Divide both sides by 3: \[ w < 1 \]

Now we combine the solutions from both inequalities:

• The first inequality gives us \( w \geq 2 \).
• The second inequality gives us \( w < 1 \).

Expressing this as a compound inequality, we get:

\[ w < 1 \quad \text{or} \quad w \geq 2 \]

Thus, the final solution is: \[ \boxed{(-\infty, 1) \cup [2, \infty)} \]