To determine which of the inequalities Preston solved based on the information provided, we start by noting the key features described:
- A closed point is plotted on the number line between 1 and 2. This suggests that the solution includes that point (the solution is equal to this value).
- The rightward arrow indicates that the solution extends to the right indefinitely, suggesting that any number greater than or equal to the point should satisfy the inequality.
Given these observations, we can analyze the provided inequalities:
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0.9x + 2.8 ≤ 5.95: Simplifying this, we get \(0.9x ≤ 3.15\) which implies \(x ≤ 3.5\). The left side does not indicate a closed interval that goes to the right.
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2.1x + 5.6 ≥ 8.75: Simplifying this gives \(2.1x ≥ 3.15\) which implies \(x ≥ 1.5\). This is consistent with a solution that includes 1.5 and goes right.
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5.6x - 18.9 ≤ 0.7: Simplifying gives \(5.6x ≤ 19.6\) that leads to \(x ≤ 3.5\). Like the first one, this doesn't cater to a rightward solution.
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3.4x - 1.2 ≥ 4.75: Simplifying leads to \(3.4x ≥ 5.95\) which gives \(x ≥ 1.75\). Similar to the second option, this allows for values greater than and equal to 1.75.
Among the presented inequalities, the second option:
2.1x + 5.6 ≥ 8.75 (which simplifies to \(x ≥ 1.5\)), is the best fit to describe a solution that includes a point between 1 and 2 and extends to the right.
Thus, the inequality Preston solved is:
2.1x + 5.6 ≥ 8.75.