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 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 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 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 \( \frac{24}{4.8} \): \[ \frac{24}{4.8} = 5 \]

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

Now, we need to identify the correct graph corresponding to this solution.

• The solution \( x \geq 5 \) indicates that we should have a closed point (or dot) at 5 and an arrow pointing to the right, indicating all values greater than or equal to 5.

Looking at the options presented:

1. The first option has a closed point at 0.5 with a leftward arrow (incorrect).
2. The second option has a closed point at 5 with a rightward arrow (correct).
3. The third option has a closed point at 5 with a leftward arrow (incorrect).
4. The fourth option has a closed point at 19.2 with a rightward arrow (incorrect).

Therefore, the correct graph that shows the solution \( x \geq 5 \) is the second option:

• 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.