Question

1. which number line represents the solution to the inequality 5 - 3x ≤ 11? f. number line f g. number line g h. number line h j. number line j

Explanation:

Step1: Solve the inequality \(5 - 3x \leq 11\)

Subtract 5 from both sides: \(5 - 3x - 5 \leq 11 - 5\)
Simplify: \(-3x \leq 6\)

Step2: Divide both sides by -3 (reverse inequality sign)

\(\frac{-3x}{-3} \geq \frac{6}{-3}\)
Simplify: \(x \geq -2\)

Step3: Analyze the number lines

• Option F: Closed dot at -2, shading to the right (since \(x \geq -2\) means all numbers greater than or equal to -2, which is right of -2 on the number line).
• Option H: Open dot at -2 (incorrect, as \(x \geq -2\) includes -2, so closed dot needed).
• Option G: Shading to the left (incorrect, should be right for \(x \geq -2\)).
• Option J: Closed dot at 2, shading right (incorrect, solution is \(x \geq -2\), not \(x \geq 2\)).

Answer:

F. The number line with a closed dot at -2 and shading to the right.