To determine which inequality Preston solved based on the number line described, we can analyze the closed point plotted between 1 and 2, along with the rightward arrow extending beyond 10. The closed point indicates that the value is included in the solution set, and the rightward arrow suggests that the solution includes all values greater than or equal to that point.
Since the point is between 1 and 2, we can infer that it is likely around 1.5 or so. Because the rightward arrow extends beyond 10, it suggests that the solution encompasses all values from this point onwards.
Next, we'll check each of the provided inequalities.
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0.9x + 2.8 ≤ 5.95
- Solving for x: \( 0.9x \leq 5.95 - 2.8 \) \( 0.9x \leq 3.15 \) \( x \leq \frac{3.15}{0.9} \approx 3.5 \)
- This does not match since it is leftward and does not go beyond 10.
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5.6x - 18.9 ≤ 0.7
- Solving for x: \( 5.6x \leq 0.7 + 18.9 \) \( 5.6x \leq 19.6 \) \( x \leq \frac{19.6}{5.6} \approx 3.5 \)
- This also does not match since it is leftward.
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3.4x - 1.2 ≥ 4.75
- Solving for x: \( 3.4x \geq 4.75 + 1.2 \) \( 3.4x \geq 5.95 \) \( x \geq \frac{5.95}{3.4} \approx 1.75 \)
- This inequality has a rightward solution from around 1.75, which matches with a rightward arrow that goes beyond 10.
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2.1x + 5.6 ≥ 8.75
- Solving for x: \( 2.1x \geq 8.75 - 5.6 \) \( 2.1x \geq 3.15 \) \( x \geq \frac{3.15}{2.1} \approx 1.5 \)
- This also has a rightward solution but is less than the previous one.
Given this analysis, the most appropriate inequality that Preston solved, which correlates with the closed point on the number line as well as the rightward arrow beyond 10, is:
3.4x - 1.2 ≥ 4.75
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