Question

solve for x and graph the solution on the number line below.
8 > 3x + 5 or 3x + 5 ≥ 29

Explanation:

Step1: Solve \( 8 > 3x + 5 \)

Subtract 5 from both sides: \( 8 - 5 > 3x + 5 - 5 \) → \( 3 > 3x \)
Divide by 3: \( \frac{3}{3} > \frac{3x}{3} \) → \( 1 > x \) or \( x < 1 \)

Step2: Solve \( 3x + 5 \geq 29 \)

Subtract 5: \( 3x + 5 - 5 \geq 29 - 5 \) → \( 3x \geq 24 \)
Divide by 3: \( \frac{3x}{3} \geq \frac{24}{3} \) → \( x \geq 8 \)

Step3: Combine solutions

The solutions are \( x < 1 \) or \( x \geq 8 \)

Answer:

\( x < 1 \) or \( x \geq 8 \)