Question

Question

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.

Answer 1

To solve the inequality \( 23x \leq 5 \), we first divide both sides by 23:

\[ x \leq \frac{5}{23} \]

Calculating \(\frac{5}{23}\) yields approximately \(0.217\), which is between \(0\) and \(1\).

The solution to the inequality indicates that \(x\) can take any value less than or equal to \(\frac{5}{23}\). Therefore, on a number line, we need a closed point (indicating that \(\frac{5}{23}\) is included in the solution) at approximately \(0.217\), with a leftward arrow extending indefinitely to the left.

Looking at the options you provided, we need to identify the option with a closed circle at \(3 \frac{1}{3}\) (which is \(3.333...\)), \(4 \frac{1}{3}\) (which is \(4.333...\)), \(5 \frac{2}{3}\) (which is \(5.666...\)), or \(7.5\) instead.

None of these points reflect \( \frac{5}{23} \) accurately. Therefore, none of the provided graphs show the correct solution.

However, based on typical representations, if any option had a point at or near \(0.217\) with a leftward arrow, that would represent the correct graph for the solution.

In conclusion: Since none of the options listed match the solution \(x \leq \frac{5}{23}\), there doesn't seem to be a correct graph choice among the provided responses.