To determine which inequality corresponds to the graph described, we need to analyze the placement of the closed point and the direction of the arrow.
- The closed point is located between 1 and 2, indicating a solution set that includes a specific number within that range.
- The rightward arrow indicates that the solution extends to values greater than that closed point, effectively representing values greater than or equal to that specific point.
Now, let's solve each inequality option step by step to find the value represented at the closed point:
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For the inequality 0.9x + 2.8 ≤ 5.95: \[ 0.9x \leq 5.95 - 2.8 \ 0.9x \leq 3.15 \ x \leq \frac{3.15}{0.9} \ x \leq 3.5 \] This solution represents values less than or equal to approximately 3.5.
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For the inequality 5.6x − 18.9 ≤ 0.7: \[ 5.6x \leq 0.7 + 18.9 \ 5.6x \leq 19.6 \ x \leq \frac{19.6}{5.6} \ x \leq 3.5 \] This solution also represents values less than or equal to approximately 3.5.
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For the inequality 2.1x + 5.6 ≥ 8.75: \[ 2.1x \geq 8.75 - 5.6 \ 2.1x \geq 3.15 \ x \geq \frac{3.15}{2.1} \ x \geq 1.5 \] This solution indicates values greater than or equal to approximately 1.5.
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For the inequality 3.4x − 1.2 ≥ 4.75: \[ 3.4x \geq 4.75 + 1.2 \ 3.4x \geq 5.95 \ x \geq \frac{5.95}{3.4} \ x \geq 1.75 \] This means values greater than or equal to approximately 1.75.
Among these inequalities, the third option, 2.1x + 5.6 ≥ 8.75, has a solution starting at or above a point within the range described (1.5 onwards), which aligns with being to the right of a closed point between 1 and 2.
Thus, Preston solved the inequality:
2.1x + 5.6 ≥ 8.75.