To determine which inequality Preston solved, we need to analyze the information given about the number line and the plotted point.
Since a closed point is plotted between 1 and 2 (let's say it is 1.5) and there is a rightward arrow from this point indicating that the solution extends to the right, this suggests that the solution is greater than or equal to a certain value.
Now let's evaluate the given inequalities one by one to see which one could produce a graph that matches this description:
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0.9x + 2.8 ≤ 5.95
Rearranging gives:
\(0.9x ≤ 5.95 - 2.8\)
\(0.9x ≤ 3.15\)
\(x ≤ \frac{3.15}{0.9} \approx 3.5\)
(Not plausible since the graph would indicate x can be less than a maximum of 3.5, which would not extend right.) -
5.6x - 18.9 ≤ 0.7
Rearranging gives:
\(5.6x ≤ 0.7 + 18.9\)
\(5.6x ≤ 19.6\)
\(x ≤ \frac{19.6}{5.6} \approx 3.5\)
(Also suggests maximum value, not rightward extension.) -
3.4x - 1.2 ≥ 4.75
Rearranging gives:
\(3.4x ≥ 4.75 + 1.2\)
\(3.4x ≥ 5.95\)
\(x ≥ \frac{5.95}{3.4} \approx 1.75\)
(This indicates values are greater than 1.75, which would extend to the right.) -
2.1x + 5.6 ≥ 8.75
Rearranging gives:
\(2.1x ≥ 8.75 - 5.6\)
\(2.1x ≥ 3.15\)
\(x ≥ \frac{3.15}{2.1} \approx 1.5\)
(This also suggests values greater than or equal to approximately 1.5, extending right.)
Among these, the inequalities that suggest the solution is greater than or equal to a certain value (and hence extend right on the number line) are option 3 and option 4.
Since the closed point is noted to be between 1 and 2, indicating it might include values close to 1.5, the inequality that matches that best would be:
3.4x - 1.2 ≥ 4.75.
Thus, the final answer to the problem is:
3.4x - 1.2 ≥ 4.75.
1 answer