Question
Inequalities Unit Test
9 of 159 of 15 Items
Question
Use the image to answer the question.
A number line is shown ranging from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line between 1 and 2. A rightward arrow is marked on the number line that originates at the closed point and goes beyond 10.
Preston solved an inequality and graphed the solution on the number line. Which of the following inequalities did he solve?
(1 point)
Responses
5.6x−18.9≤0.7
5.6 x minus 18.9 less than or equal to 0.7
0.9x+2.8≤5.95
0.9 x plus 2.8 less than or equal to 5.95
3.4x−1.2≥4.75
3.4 x minus 1.2 greater than or equal to 4.75
2.1x+5.6≥8.75
9 of 159 of 15 Items
Question
Use the image to answer the question.
A number line is shown ranging from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line between 1 and 2. A rightward arrow is marked on the number line that originates at the closed point and goes beyond 10.
Preston solved an inequality and graphed the solution on the number line. Which of the following inequalities did he solve?
(1 point)
Responses
5.6x−18.9≤0.7
5.6 x minus 18.9 less than or equal to 0.7
0.9x+2.8≤5.95
0.9 x plus 2.8 less than or equal to 5.95
3.4x−1.2≥4.75
3.4 x minus 1.2 greater than or equal to 4.75
2.1x+5.6≥8.75
Answers
GPT-4o mini
To determine which inequality Preston solved based on the description of the number line, we need to analyze the indicated closed point and the direction of the arrow.
1. **Closed Point:** The closed point is between 1 and 2, which implies that the solution includes this value. This suggests that the inequality is either \( \leq \) (less than or equal to) or \( \geq \) (greater than or equal to).
2. **Rightward Arrow:** A rightward arrow indicates that the values continue to increase beyond the closed point. This suggests that the inequality solution is greater than or equal to the value at the closed point.
Now, let's examine each of the provided inequalities:
- **A. \( 5.6x - 18.9 \leq 0.7 \)**: This would imply solutions less than or equal to some value, which does not match the rightward arrow.
- **B. \( 0.9x + 2.8 \leq 5.95 \)**: Similar to option A, this suggests values less than or equal to a certain point, not consistent with the rightward direction.
- **C. \( 3.4x - 1.2 \geq 4.75 \)**: This indicates values greater than or equal to a certain point, which aligns with the rightward arrow.
- **D. \( 2.1x + 5.6 \geq 8.75 \)**: This also indicates values greater than or equal to a specific value, which matches the rightward direction but would need more specific solving to pinpoint.
Given the cues from the number line, the most suitable response is:
**3.4x - 1.2 ≥ 4.75** (Option C), as it fits the condition of having a closed point and extending rightward on the number line.
1. **Closed Point:** The closed point is between 1 and 2, which implies that the solution includes this value. This suggests that the inequality is either \( \leq \) (less than or equal to) or \( \geq \) (greater than or equal to).
2. **Rightward Arrow:** A rightward arrow indicates that the values continue to increase beyond the closed point. This suggests that the inequality solution is greater than or equal to the value at the closed point.
Now, let's examine each of the provided inequalities:
- **A. \( 5.6x - 18.9 \leq 0.7 \)**: This would imply solutions less than or equal to some value, which does not match the rightward arrow.
- **B. \( 0.9x + 2.8 \leq 5.95 \)**: Similar to option A, this suggests values less than or equal to a certain point, not consistent with the rightward direction.
- **C. \( 3.4x - 1.2 \geq 4.75 \)**: This indicates values greater than or equal to a certain point, which aligns with the rightward arrow.
- **D. \( 2.1x + 5.6 \geq 8.75 \)**: This also indicates values greater than or equal to a specific value, which matches the rightward direction but would need more specific solving to pinpoint.
Given the cues from the number line, the most suitable response is:
**3.4x - 1.2 ≥ 4.75** (Option C), as it fits the condition of having a closed point and extending rightward on the number line.