se the image to answer the question. 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+212<212 x plus 2 Start Fraction 1 over 2 End Fraction less than 2 Start Fraction 1 over 2 End Fraction x−213<216 x minus 2 Start Fraction 1 over 3 End Fraction less than 2 Start Fraction 1 over 6 End Fraction x+1.25≤5.75
use the image to answer the question. 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+212<212 x plus 2 Start Fraction 1 over 2 End Fraction less than 2 Start Fraction 1 over 2 End Fraction x−213<216 x minus 2 Start Fraction 1 over 3 End Fraction less than 2 Start Fraction 1 over 6 End Fraction x+1.25≤5.75
The line graph starts at -10 then ends at 10 there is an open circle in between 4 and 5,Which of the following inequalities did she solve?
Based on the information you provided about the number line graph, there is an open circle between 4 and 5. An open circle typically represents that the number at that point is not included in the solution set, which corresponds to a "less than" (<) or "greater than" (>) inequality, rather than a "less than or equal to" (≤) or "greater than or equal to" (≥) inequality.
Let's evaluate the provided inequalities to find the one that matches this description:
1. \( x - 1.5 \leq 3 \)
This inequality includes "less than or equal to" (≤), which would be represented with a closed circle, not an open one. So, this is not the correct inequality.
2. \( x + \frac{2}{12} < \frac{25}{12} \)
This inequality includes "less than" (<), which would be represented with an open circle. However, when reduced, the fraction \( \frac{25}{12} \) is greater than 2, not between 4 and 5. So, this is not the correct inequality.
3. \( x - \frac{2}{3} < \frac{2}{6} \)
This inequality also includes "less than" (<), and the fraction \( \frac{2}{6} \) simplifies to \( \frac{1}{3} \). When solving for x, we would add \( \frac{2}{3} \) to both sides, giving us \( x < 1 \). This is also not the correct inequality, as it does not match the open circle between 4 and 5.
4. \( x + 1.25 \leq 5.75 \)
Even though this inequality includes "less than or equal to" (≤), which typically corresponds to a closed circle, let's solve it and check the number:
\( x \leq 5.75 - 1.25 \)
\( x \leq 4.5 \)
This inequality states that x is less than or equal to 4.5, which at first glance seems to correspond to the description of the graph with a circle at a point between 4 and 5. However, because the circle is open, it should not be "less than or equal to."
Given that none of the provided inequalities strictly matches the description of an open circle between 4 and 5, there may be either a typo in your description of the inequalities or the graph. If the circle is indeed open, the correct inequality would be one that involves "less than" at a value between 4 and 5, but none of the options exactly represent that scenario with an open circle.
If the inequality actually corresponds to the point 4.5 with an open circle, there may be a mistake in the listed options since none of the "less than" inequalities reflect that. However, if the circle is meant to be closed (and there was a mistake in the description of the graph), then the correct inequality would be the fourth one: \( x + 1.25 \leq 5.75 \), as it solves to \( x \leq 4.5 \).
Use the image to answer the question. Willow solved an inequality and graphed the solution on the number line. Which of the following inequalities did she solve? (1 point)
The line graph starts at -10 then ends at 10 there is an open circle in between 4 and 5, and the colored line is heading towards -1.Which of the following inequalities did she solve?
Based on the additional description you provided indicating that there is an open circle between 4 and 5 and that the colored line is heading towards -10 (which I assume means to the left from the open circle towards negative values), we can deduce the following about the inequality:
1. Since there is an open circle, the inequality should involve a "less than" (<) symbol rather than a "less than or equal to" (≤).
2. Because the colored line extends left from the open circle towards -10, the inequality represents that x is less than the value where the open circle is located.
Given the open circle is between 4 and 5, the value where the circle is located is likely 4.5, considering standard number lines and the provided options.
Now let's check the provided inequalities and see which fits this description:
1. \( x - 1.5 \leq 3 \) would have a closed circle due to the "less than or equal to" (≤) symbol, so it is not a match.
2. \( x + \frac{2}{12} < \frac{25}{12} \) reduces to \( x + \frac{1}{6} < \frac{25}{12} \) where \( \frac{25}{12} \) simplifies to 2.08 (approximately). This inequality also does not have an open circle at 4.5, so it is not a match.
3. \( x - \frac{2}{3} < \frac{2}{6} \) which simplifies to \( x - \frac{2}{3} < \frac{1}{3} \). This solves to \( x < 1 \), which does not match an open circle at 4.5 and a line extending left, so it is not a match.
4. It seems you have referenced an inequality \( x + 1.25 \leq 5.75 \) in earlier messages, but based on your current description, we should look for an inequality with "less than" (<) instead of "less than or equal to" (≤). However, since you have not listed the complete inequality in this instance, we cannot evaluate it properly.
Since none of the listed complete inequalities matches an open circle at 4.5 with the line extending left (towards negative numbers), there may be a mistake in the provided options or in the description of the graph. If the correct inequality was listed but the description of the "less than or greater than" symbol was incorrect, we would solve the inequality \( x + 1.25 < 5.75 \), which would result in \( x < 4.5 \), with an open circle at 4.5 and the solution set extending to the left, which would match your description.
However, without the full correct inequality listed, I can only provide a logical guess based on the information given. If you're able to supply the complete inequality in question this time, I can confirm the exact answer for you.
Use the image to answer the question. Willow solved an inequality and graphed the solution on the number line. Which of the following inequalities did she solve? (1 point)
The line graph starts at -10 then ends at 10 there is an open circle in between 4 and 5, and the colored line is heading towards -1.Which of the following inequalities did she solve?
Answers:
x−1.5≤3
x + 2 1/2 < 2 1/2
x - 2 1/3 < 2 1/6
x + 1.25 ≤ 5.75
Given the following options:
- \( x - 1.5 \leq 3 \)
- \( x + 2\frac{1}{2} < 2\frac{1}{2} \)
- \( x - 2\frac{1}{3} < 2\frac{1}{6} \)
- \( x + 1.25 \leq 5.75 \)
And the information that the number line graph has an open circle between 4 and 5 and the colored line is heading towards -10 (to the left), let's solve the inequalities to determine which one matches the graph:
1. \( x - 1.5 \leq 3 \)
Adding 1.5 to both sides gives us \( x \leq 4.5 \). This inequality implies that the graph should have a *closed* circle at 4.5, extending to the left. This doesn't match because the circle should be open.
2. \( x + 2\frac{1}{2} < 2\frac{1}{2} \)
Subtracting \( 2\frac{1}{2} \) from both sides gives us \( x < 0 \). This inequality implies that there should be an open circle at 0, extending to the left. This doesn't match the description of an open circle between 4 and 5.
3. \( x - 2\frac{1}{3} < 2\frac{1}{6} \)
Converting mixed numbers to improper fractions gives us \( x - \frac{7}{3} < \frac{13}{6} \). Multiplying 6 to both sides to eliminate the fractions gives \( 6x - 14 < 13 \), implying that \( 6x < 27 \) or \( x < 4.5 \). This inequality implies there should be an open circle at 4.5, extending to the left, which matches the given description of the graph.
4. \( x + 1.25 \leq 5.75 \)
Subtracting 1.25 from both sides gives us \( x \leq 4.5 \). This inequality implies that there should be a closed circle at 4.5, extending to the left, which does not match because the circle should be open.
Given the description, the correct inequality that Willow solved is most likely the third option:
\( x - 2\frac{1}{3} < 2\frac{1}{6} \)
This results in a graph with an open circle around 4.5, with the line extending to the left (towards negative numbers), which matches the given characteristics of the number line graph.
i gave u the answer choices, which one of em is it?
My apologies for any confusion. With the provided answer choices and the description of the number line, the correct inequality Willow solved is:
\( x - 2\frac{1}{3} < 2\frac{1}{6} \)
Recalculating this with the proper approach, we need to:
1. Convert mixed numbers to improper fractions: \( 2\frac{1}{3} \) becomes \( \frac{7}{3} \) and \( 2\frac{1}{6} \) becomes \( \frac{13}{6} \).
2. Write the inequality with improper fractions: \( x - \frac{7}{3} < \frac{13}{6} \).
3. Find a common denominator, which is 6, so we will adjust the fraction on the left accordingly: \( x - \frac{14}{6} < \frac{13}{6} \).
4. Isolate x by adding \( \frac{14}{6} \) to both sides: \( x < \frac{13}{6} + \frac{14}{6} \).
5. Add the fractions: \( x < \frac{27}{6} \).
6. Simplify the fraction: \( x < \frac{27}{6} \) becomes \( x < 4.5 \).
The inequality \( x - 2\frac{1}{3} < 2\frac{1}{6} \) translates to \( x < 4.5 \) when simplified. The solution on the number line would be an open circle at 4.5 with the shaded area extending left towards lower numbers, which corresponds to your described graph. Hence, this is the inequality that matches the number line graph.
Apologies, but as an AI text-based interface, I'm unable to interpret visual content such as images directly. However, I can help you evaluate each of the provided inequalities to see which one could match what you describe from the image of the number line graph.
Let's examine each of the inequalities:
1. \( x - 1.5 \leq 3 \)
To solve this inequality for x, we can add 1.5 to both sides:
\( x \leq 3 + 1.5 \)
\( x \leq 4.5 \)
This means x can be any number less than or equal to 4.5.
2. \( x + \frac{2}{12} < \frac{25}{12} \)
Since \( \frac{2}{12} \) simplifies to \( \frac{1}{6} \), the inequality becomes:
\( x + \frac{1}{6} < \frac{25}{12} \)
To solve for x, subtract \( \frac{1}{6} \) or \( \frac{2}{12} \) from \( \frac{25}{12} \) to find the boundary for x:
\( x < \frac{25}{12} - \frac{2}{12} \)
\( x < \frac{23}{12} \)
Converted to decimal form, \( x < 1.916\bar{6} \), where the overline denotes a repeating decimal.
3. \( x - \frac{2}{3} < \frac{2}{6} \)
Since \( \frac{2}{6} \) simplifies to \( \frac{1}{3} \), the inequality becomes:
\( x - \frac{2}{3} < \frac{1}{3} \)
To solve for x, you would add \( \frac{2}{3} \) to both sides:
\( x < \frac{1}{3} + \frac{2}{3} \)
\( x < 1 \)
So x can be any number less than 1.
4. \( x + 1.25 \leq 5.75 \)
Subtract 1.25 from both sides to solve for x:
\( x \leq 5.75 - 1.25 \)
\( x \leq 4.5 \)
This means x can be any number less than or equal to 4.5.
Based on the solutions to the inequalities:
- For the first inequality, x is any number less than or equal to 4.5.
- For the second inequality, x is any number less than approximately 1.917.
- For the third inequality, x is any number less than 1.
- For the fourth inequality, x is also any number less than or equal to 4.5.
If the graph on the number line that you're referring to matches one of these solutions, then that inequality would be the one Willow solved. Without seeing the graph, though, I cannot determine which of these solutions matches the graphed solution, and it's also important to note that options 1 and 4 have the same algebraic solution. If there is a specific characteristic of the graph that you could describe (such as where the shading is or whether there is an open or closed circle at the endpoint), I could help you determine which inequality she solved.