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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 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.

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 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 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.

1 answer

To solve the inequality \( 23x \leq 5 \), we start by isolating \( x \):

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

Next, we need to find out what \( \frac{5}{23} \) is in decimal form to better understand its location on the number line: \[ \frac{5}{23} \approx 0.217 \]

Thus, the solution to the inequality \( x \leq \frac{5}{23} \) means \( x \) can take any value less than or equal to approximately 0.217.

Now we look for the graph that corresponds to this solution:

  • We need a closed point (indicating \( \leq \)) at \( \frac{5}{23} \), which is about \( 0.217 \).
  • The graph should have a leftward arrow indicating all values less than or equal to \( \frac{5}{23} \).

The first option you provided has a closed point plotted at \( \frac{5}{3} \), which is incorrect. The second option is at \( 7.5 \), which is also incorrect. The third option has a closed point at \( \frac{4}{3} \), which again is incorrect. The fourth option is at \( \frac{10}{3} \), which is also incorrect.

None of the provided options represent the appropriate graph for the inequality \( 23x \leq 5 \) since none mention or show the point at \( \frac{5}{23} \) (approximately \( 0.217 \)). It seems like the correct graph is missing from your options.

To summarize, the solution to the inequality is \( x \leq \frac{5}{23} \) and should be represented as a closed point around \( 0.217 \) with a leftward arrow on the number line.