Question

Preston solved an inequality and graphed the solution on the number line. Which of the following inequalities did he solve?

(1 point)

A. 2.1x+5.6≥8.75

B. 0.9x+2.8≤5.95

C. 5.6x−18.9≤0.7

D. 3.4x−1.2≥4.75

Answer 1

To determine which inequality Preston solved, we need to analyze each option and solve them for \(x\).

### A. \(2.1x + 5.6 ≥ 8.75\)
1. Subtract \(5.6\) from both sides:
\[
2.1x ≥ 8.75 - 5.6
\]
\[
2.1x ≥ 3.15
\]
2. Divide both sides by \(2.1\):
\[
x ≥ \frac{3.15}{2.1} \approx 1.5
\]

### B. \(0.9x + 2.8 ≤ 5.95\)
1. Subtract \(2.8\) from both sides:
\[
0.9x ≤ 5.95 - 2.8
\]
\[
0.9x ≤ 3.15
\]
2. Divide both sides by \(0.9\):
\[
x ≤ \frac{3.15}{0.9} \approx 3.5
\]

### C. \(5.6x - 18.9 ≤ 0.7\)
1. Add \(18.9\) to both sides:
\[
5.6x ≤ 0.7 + 18.9
\]
\[
5.6x ≤ 19.6
\]
2. Divide both sides by \(5.6\):
\[
x ≤ \frac{19.6}{5.6} \approx 3.5
\]

### D. \(3.4x - 1.2 ≥ 4.75\)
1. Add \(1.2\) to both sides:
\[
3.4x ≥ 4.75 + 1.2
\]
\[
3.4x ≥ 5.95
\]
2. Divide both sides by \(3.4\):
\[
x ≥ \frac{5.95}{3.4} \approx 1.75
\]

### Summary of Results:
- A: \(x \geq 1.5\)
- B: \(x \leq 3.5\)
- C: \(x \leq 3.5\)
- D: \(x \geq 1.75\)

Since the prompts mention that Preston solved an inequality and graphed it on the number line, look for the one with a distinct range that could be visible on such a graph.

If you provide the specific graph Preston created, we could identify the correct option among A, B, C, and D more accurately.