Solve the inequality 4.8x≥24

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 0.5. 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 0.5. 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 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 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 5. A rightward arrow is marked on the number line that originates at the closed circle and goes beyond 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. A rightward arrow is marked on the number line that originates at the closed circle and goes beyond 10.

A number line ranges from 5 to 25 with numbers listed in unit increments. A closed point is plotted on the number line at 19.2. A rightward arrow is marked on the number line that originates at the closed circle and goes beyond 25.

Answer 1

To solve the inequality \(4.8x \geq 24\), we start by isolating \(x\).

1. Divide both sides by \(4.8\): \[ x \geq \frac{24}{4.8} \]
2. Calculate \(\frac{24}{4.8}\): \[ \frac{24}{4.8} = 5 \]

So the solution to the inequality is: \[ x \geq 5 \]

This means \(x\) is greater than or equal to 5.

Now, we need to identify which graph correctly represents this solution:

• The graph should have a closed circle at 5 (indicating that 5 is included) and an arrow extending to the right (indicating that values greater than 5 are included).

From the given options, the one that shows a closed point at 5 and a rightward arrow beyond 10 is the correct representation of the solution:

The correct choice is:

• 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. A rightward arrow is marked on the number line that originates at the closed circle and goes beyond 10.