Question
A number line with arrows at both the ends ranges from negative 10 to 10 in unit increments. An open circle is marked on the number line at 4.5. A line is drawn from the circle toward negative 10 with an arrow at the end.
Willow solved an inequality and graphed the solution on the number line. Which of the following inequalities did she solve?
(1 point)
Responses
x−1.5≤3
x minus 1.5 less-than-or-equal-to 3
x+2 1/2<2 1/2
x plus 2 Start Fraction 1 over 2 End Fraction less than 2 Start Fraction 1 over 2 End Fraction
x+1.25≤5.75
x plus 1.25 less-than-or-equal-to 5.75
x−2 1/3<2 1/6
Willow solved an inequality and graphed the solution on the number line. Which of the following inequalities did she solve?
(1 point)
Responses
x−1.5≤3
x minus 1.5 less-than-or-equal-to 3
x+2 1/2<2 1/2
x plus 2 Start Fraction 1 over 2 End Fraction less than 2 Start Fraction 1 over 2 End Fraction
x+1.25≤5.75
x plus 1.25 less-than-or-equal-to 5.75
x−2 1/3<2 1/6
Answers
GPT-4o mini
To determine which inequality corresponds to the graph description, we need to analyze the number line provided. An open circle at 4.5 means that the value 4.5 is not included in the solution, and a line drawn toward negative 10 indicates that the solution contains all values less than 4.5.
Let's rewrite the inequality that represents the situation described on the number line. Since the line extends left towards negative infinity without including 4.5, the inequality that represents this situation is:
\[ x < 4.5 \]
Now, we will solve each of the given inequalities to see which one results in the solution \( x < 4.5 \).
1. **For the inequality \( x−1.5≤3 \)**:
\[
x - 1.5 \leq 3 \\
x \leq 3 + 1.5 \\
x \leq 4.5
\]
This solution includes \( 4.5 \), so it does not match.
2. **For the inequality \( x + 2 \frac{1}{2} < 2 \frac{1}{2} \)**:
\[
x + 2.5 < 2.5 \\
x < 2.5 - 2.5 \\
x < 0
\]
This is also incorrect.
3. **For the inequality \( x + 1.25 ≤ 5.75 \)**:
\[
x + 1.25 \leq 5.75 \\
x \leq 5.75 - 1.25 \\
x \leq 4.5
\]
Again, this solution includes \( 4.5 \), so it does not match.
4. **For the inequality \( x−2 \frac{1}{3}<2 \frac{1}{6} \)**:
\[
x - 2.33 < 2.10 \\
x < 2.10 + 2.33 \\
x < 4.43
\]
This solution is also valid but not equivalent to our desired condition.
Based on the analysis, none of the inequalities clearly correspond to the condition \( x < 4.5 \) as an open circle on the number line denotes. Typically, we would expect a solution such that \(x < 4.5\), resulting in a closed circle at exactly 4.5 and an arrow extending to the left toward negative infinity.
Since the closest inequalities could include values less than or approaching 4.5 while not including it, if we reevaluate, **the option that keeps values less than or another near the 4.5 would have been the exact fit** if provided. But among these options, the one ensuring that \(x\) is the least but approximately down to our direction full to closure will be \( x - 1.5 ≤ 3\) as it reaches precisely to closure least values towards \( 4.5 \).
Thus, the most appropriate answer based on these inequalities is:
**\( x - 1.5 ≤ 3 \)**.
So, **Willow solved \( x-1.5≤3 \)**.
Let's rewrite the inequality that represents the situation described on the number line. Since the line extends left towards negative infinity without including 4.5, the inequality that represents this situation is:
\[ x < 4.5 \]
Now, we will solve each of the given inequalities to see which one results in the solution \( x < 4.5 \).
1. **For the inequality \( x−1.5≤3 \)**:
\[
x - 1.5 \leq 3 \\
x \leq 3 + 1.5 \\
x \leq 4.5
\]
This solution includes \( 4.5 \), so it does not match.
2. **For the inequality \( x + 2 \frac{1}{2} < 2 \frac{1}{2} \)**:
\[
x + 2.5 < 2.5 \\
x < 2.5 - 2.5 \\
x < 0
\]
This is also incorrect.
3. **For the inequality \( x + 1.25 ≤ 5.75 \)**:
\[
x + 1.25 \leq 5.75 \\
x \leq 5.75 - 1.25 \\
x \leq 4.5
\]
Again, this solution includes \( 4.5 \), so it does not match.
4. **For the inequality \( x−2 \frac{1}{3}<2 \frac{1}{6} \)**:
\[
x - 2.33 < 2.10 \\
x < 2.10 + 2.33 \\
x < 4.43
\]
This solution is also valid but not equivalent to our desired condition.
Based on the analysis, none of the inequalities clearly correspond to the condition \( x < 4.5 \) as an open circle on the number line denotes. Typically, we would expect a solution such that \(x < 4.5\), resulting in a closed circle at exactly 4.5 and an arrow extending to the left toward negative infinity.
Since the closest inequalities could include values less than or approaching 4.5 while not including it, if we reevaluate, **the option that keeps values less than or another near the 4.5 would have been the exact fit** if provided. But among these options, the one ensuring that \(x\) is the least but approximately down to our direction full to closure will be \( x - 1.5 ≤ 3\) as it reaches precisely to closure least values towards \( 4.5 \).
Thus, the most appropriate answer based on these inequalities is:
**\( x - 1.5 ≤ 3 \)**.
So, **Willow solved \( x-1.5≤3 \)**.