Solve the inequality 23x≤5

Question

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

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.
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Answer 1

To solve the inequality $23x\le 5$, we first isolate $x$:

1. Divide both sides by 23: $$x\le \frac{5}{23}$$

Next, we need to calculate the decimal value of $\frac{5}{23}$: $$\frac{5}{23}\approx 0.2174$$

Thus, the solution to the inequality is: $$x\le 0.2174$$

On a number line, this means we have a closed circle at approximately $0.2174$ (or $\frac{5}{23}$), with a leftward arrow indicating that all values to the left of this point are included in the solution.

Now, looking at your provided options, we need to find the graph that has a closed circle at $\frac{5}{23}$ or close to it, and extends to the left.

From your options:

• None of the exact fractions provided in the options are $\frac{5}{23}$, but you can compare the decimal values and see which fraction appears closest to $0.2174$.
• $4\frac{1}{3}$ is approximately $4.33$ (not correct)
• $5\frac{2}{3}$ is approximately $5.67$ (not correct)
• $7.5$ (not correct)
• $3\frac{1}{3}$ is approximately $3.33$ (not correct)

It seems that none of the points described correspond to $\frac{5}{23}\approx 0.2174$. In a typical context where you're asked for approximately $\frac{5}{23}$, it could be presented more clearly.

However, since the requirement is that the point is closed and that it is less than or equal to the number you have — the correct graph should have a point left of $1$ that indicates all numbers less than that point including the point itself.

If you can determine which option represents a number close to 0.2174, that would represent $x\le \frac{5}{23}$ correctly. If none match, there may be an issue in the options provided.