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Solve the inequality 23x≤5

. Which of the following graphs shows the solution? (1 point)
Responses

1.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.

2.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.

3.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.

4.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.

2 answers

To solve the inequality \( 23x \leq 5 \):

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

  2. Now, we need to consider what \( \frac{5}{23} \) is as a decimal. Calculating it gives: \[ \frac{5}{23} \approx 0.217 \]

Thus, the solution to the inequality is \( x \leq \frac{5}{23} \).

Now we need to check which of the options provides the correct representation on the number line:

  • We are looking for a closed point at \( \frac{5}{23} \) or approximately \( 0.217 \), with a leftward arrow indicating values less than or equal to this point.

Among the options provided:

  • Option 1 has a point at \( \frac{5}{3} \) (approximately \( 1.67 \)) - this is too high.
  • Option 2 has a point at \( \frac{10}{3} \) (approximately \( 3.33 \)) - this is too high.
  • Option 3 has a point at \( \frac{13}{3} \) (approximately \( 4.33 \)) - this is too high.
  • Option 4 has a point at \( 7.5 \) - this is also too high.

None of the options provided contain the correct point \( \frac{5}{23} \) or \( 0.217 \). Please check the options again, as they appear to be incorrect for the solution to the inequality \( 23x \leq 5 \).

just pick one