Solve the inequality 23x≤5

Question

. 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 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 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.

Answer 1

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

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

Now we need to find the decimal or fraction equivalent of \(\frac{5}{23}\) to locate it on the number line.

The calculation of \(\frac{5}{23}\) gives approximately \(0.217\), which can also be expressed as approximately \(0.22\) (to 2 decimal places).

Next, on a number line, \(\frac{5}{23}\) will be represented as a closed circle at that point, and because the inequality shows \(x\) is less than or equal to \(\frac{5}{23}\), there will be a leftward arrow extending from it.

Among the options provided, you will want to see which closed point on the number line is at \(\frac{5}{23}\) (approximately \(0.217\)) and has a leftward arrow from that point.

If none of the closed points in the options match \(\frac{5}{23}\) directly, please evaluate their numerical placements on the number line based on where they are in relation to \(0.217\).

Based on the given information, the correct choice must have a closed point at \(\frac{5}{23}\) with a leftward arrow. If you need further specificity and if available options are rounded like \(3\frac{1}{3}\) or others, identify which of those is closest numerically to \(0.217\) or \( \frac{5}{23}\).

In the responses you've given, the second option with a closed point at \(5 \frac{2}{3}\) is the best candidate if it is indeed representing \(0.217\). However, since it sounds like it's not correct, confirm which of the choices has a closed circle approximately at \(0.217\) with a leftward arrow to represent the solution of the inequality accurately.