Question

1. which number line represents the solution to the inequality 125x + 200 ≥ 1,200? a. number line a b. number line b c. number line c d. number line d

Explanation:

Step1: Solve the inequality

Start with the inequality \(125x + 200 \geq 1200\). Subtract 200 from both sides: \(125x \geq 1200 - 200\), so \(125x \geq 1000\). Then divide both sides by 125: \(x \geq \frac{1000}{125}\), which simplifies to \(x \geq 8\).

Step2: Analyze the number lines

• A number line representing \(x \geq 8\) should have a closed circle at 8 (since the inequality is "greater than or equal to") and the line shaded to the right (towards larger numbers).
• Option A: Closed circle at 8, shaded right – matches \(x \geq 8\).
• Option B: Closed circle at 8, shaded left – represents \(x \leq 8\), incorrect.
• Option C: Open circle at 8, shaded right – represents \(x > 8\), incorrect (we need "or equal to").
• Option D: Open circle at 8, shaded left – represents \(x < 8\), incorrect.

Answer:

A. The number line with a closed circle at 8 and shaded to the right (from the given options, the one labeled A with closed circle at 8 and right shading).