To determine which inequality Preston solved, we need to analyze each option and solve them for \(x\).
A. \(2.1x + 5.6 ≥ 8.75\)
- Subtract \(5.6\) from both sides: \[ 2.1x ≥ 8.75 - 5.6 \] \[ 2.1x ≥ 3.15 \]
- Divide both sides by \(2.1\): \[ x ≥ \frac{3.15}{2.1} \approx 1.5 \]
B. \(0.9x + 2.8 ≤ 5.95\)
- Subtract \(2.8\) from both sides: \[ 0.9x ≤ 5.95 - 2.8 \] \[ 0.9x ≤ 3.15 \]
- Divide both sides by \(0.9\): \[ x ≤ \frac{3.15}{0.9} \approx 3.5 \]
C. \(5.6x - 18.9 ≤ 0.7\)
- Add \(18.9\) to both sides: \[ 5.6x ≤ 0.7 + 18.9 \] \[ 5.6x ≤ 19.6 \]
- Divide both sides by \(5.6\): \[ x ≤ \frac{19.6}{5.6} \approx 3.5 \]
D. \(3.4x - 1.2 ≥ 4.75\)
- Add \(1.2\) to both sides: \[ 3.4x ≥ 4.75 + 1.2 \] \[ 3.4x ≥ 5.95 \]
- 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.
1 answer