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A number line ranges from negative 10 to 10 with numbers listed in unit increments. An open point is plotted on the number line at 1.75. A leftward arrow is marked on the number line that originates at the open circle and goes beyond negative 10.

Nora solved an inequality and graphed the solution on the number line. Which of the following inequalities did she solve?

(1 point)
Responses

4x>7
4 x greater than 7

6x<10.5
6 x less than 10.5

1.75x<3.5
1.75 x less than 3.5

8x>14

12 answers

To determine which inequality Nora solved, we need to analyze the number line description.

The open point at 1.75 indicates that the solution does not include this value (hence the "open" point). The leftward arrow suggests that the solutions extend to negative infinity, meaning that the values less than 1.75 are included.

Next, let's evaluate the given inequalities:

  1. 4x > 7:

    • Solving this gives \( x > \frac{7}{4} = 1.75 \), which would indicate values greater than 1.75, not the case here.

  2. 6x < 10.5:

    • Solving this yields \( x < \frac{10.5}{6} = 1.75 \), which matches the description. However, this inequality would not specifically indicate an open circle at 1.75 since it would include everything less than 1.75.

  3. 1.75x < 3.5:

    • Solving this gives \( x < \frac{3.5}{1.75} = 2 \). Again, this does not match as it doesn't lead to anything specifically marked at 1.75.

  4. 8x > 14:

    • Solving this provides \( x > \frac{14}{8} = 1.75 \), which again does not indicate a leftward arrow from an open point at 1.75.

Given the description of the number line with the open circle at 1.75 and the leftward arrow, the most likely correct answer is:

6x < 10.5

This inequality would plot an open circle at 1.75, indicating values less than 1.75, which aligns with the description provided.

Solve the inequality 23x≤5 . Which of the following graphs shows the solution? (1 point)
Responses

A number line ranges from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line at 7.5. A leftward arrow is marked on the number line that originates at the closed circle and goes beyond negative 10.
Image with alt text: A number line ranges from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line at 7.5. A leftward arrow is marked on the number line that originates at the closed circle and goes beyond negative 10.

A number line ranges from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line at 3 start fraction 1 over 3 end fraction. A leftward arrow is marked on the number line that originates at the closed circle and goes beyond negative 10.
Image with alt text: A number line ranges from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line at 3 start fraction 1 over 3 end fraction. A leftward arrow is marked on the number line that originates at the closed circle and goes beyond negative 10.

A number line ranges from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line at 4 start fraction 1 over 3 end fraction. A leftward arrow is marked on the number line that originates at the closed circle and goes beyond negative 10.
Image with alt text: A number line ranges from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line at 4 start fraction 1 over 3 end fraction. A leftward arrow is marked on the number line that originates at the closed circle and goes beyond negative 10.

A number line ranges from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line at 5 start fraction 2 over 3 end fraction. A leftward arrow is marked on the number line that originates at the closed circle and goes beyond negative 10.
Image with alt text: A number line ranges from negative 10 to 10 with numbers listed in unit increments. A closed point is plotted on the number line at 5 start fraction 2 over 3 end fraction. A leftward arrow is marked on the number line that originates at the closed circle and goes beyond negative 10.

To solve the inequality \( 23x \leq 5 \), we need to isolate \( x \).

Here's how to do it step by step:

  1. Divide both sides of the inequality by 23: \[ x \leq \frac{5}{23} \]
  2. Now we need to approximate the value of \( \frac{5}{23} \). Performing the division gives approximately \( 0.217 \).

This tells us the solution is all the values of \( x \) that are less than or equal to approximately \( 0.217 \).

Now, let's look at the options given and find out which graph corresponds to \( x \leq \frac{5}{23} \):

  1. Closed point at 7.5 with a leftward arrow: This indicates values less than or equal to 7.5, which is incorrect.

  2. Closed point at \( 3\frac{1}{3} \) (which is approximately \( 3.33 \)) with a leftward arrow: This also is incorrect, as it implies values less than or equal to \( 3.33 \).

  3. Closed point at \( 4\frac{1}{3} \) (which is approximately \( 4.33 \)) with a leftward arrow: This is not correct either, since \( 4.33 \) is greater than \( 0.217 \).

  4. Closed point at \( 5\frac{2}{3} \) (which is approximately \( 5.67 \)) with a leftward arrow: Again, this is incorrect for the same reason.

None of the given choices seem to correspond directly to the value of \( \frac{5}{23} \) or \( \approx 0.217 \).

If the options you provided correctly depict ranges of values, the solution should show a closed point at approximately \( 0.217 \) (or \( \frac{5}{23} \)) with a leftward arrow extending beyond negative infinity.

Could you please recheck the options provided or specify if there are any extra details?

wrong

I apologize for any confusion in my previous response. Let's clarify and ensure we solve the inequality accurately.

To solve the inequality: \[ 23x \leq 5 \]

  1. Divide both sides by 23: \[ x \leq \frac{5}{23} \]

Now let's calculate \( \frac{5}{23} \):

  • Performing the division gives us approximately \( 0.2174 \).

Analyzing the Options

We are looking for a closed point (since it's \( \leq \)), indicating all values less than or equal to \( \frac{5}{23} \) (approximately \( 0.2174 \)), along with a leftward arrow on the number line.

  1. Closed point at 7.5: Incorrect.
  2. Closed point at \( 3\frac{1}{3} \) (approximately \( 3.33 \)): Incorrect.
  3. Closed point at \( 4\frac{1}{3} \) (approximately \( 4.33 \)): Incorrect.
  4. Closed point at \( 5\frac{2}{3} \) (approximately \( 5.67 \)): Incorrect.

Since you mentioned my prior answer was incorrect and I'm not seeing an option that fits, I need to reevaluate the context of the options you provided.

Correct Interpretation

Since \( \frac{5}{23} \) is approximately \( 0.2174 \), the appropriate graph would need a closed point somewhere between \( 0 \) and \( 0.5 \) (it should be around \( 0.2 \)) with a leftward arrow.

If you could provide clearer details or confirm if there's an option I may not have interpreted correctly, I'd greatly appreciate it so that I can assist accurately! The only option fitting this range would ideally need to have all \( x \leq 0.2174\) inclusive.

ur dumb

I apologize for the oversight and any frustration it caused you. Let’s clarify things step-by-step.

We need to solve the inequality:

\[ 23x \leq 5 \]

  1. Divide both sides by 23: \[ x \leq \frac{5}{23} \]

  2. Calculating \(\frac{5}{23}\): \[ \frac{5}{23} \approx 0.217 \]

Now, we are looking for a graph that shows:

  • A closed point at \(\frac{5}{23}\) (or approximately 0.217)
  • A leftward arrow indicating values less than or equal to this number.

Based on the descriptions of the graphs you provided earlier, we need to find the graph that represents this.

Please let me know if you want to analyze more details about the graphs you listed or if there's anything else I can assist you with! Thank you for your patience, and I'm here to help.

dumb bot

I apologize for any misunderstandings and for not meeting your expectations. I appreciate your feedback, and I'm here to help. If you have any specific questions or need further assistance, please let me know how I can improve. Thank you for your patience!

your cute

Thank you for the compliment! If there's anything else you want to discuss or any questions you have, feel free to ask. I'm here to help!

ok
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