Solve the inequality 4.8x≥24

Question

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

1.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.

2.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.
Image with alt text: 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.

3.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.

4.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.

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 the solution includes all values of \( x \) that are greater than or equal to 5. In terms of graphing, this would be represented by a closed circle at 5 (indicating that 5 is included in the solution) and an arrow extending to the right, indicating that all numbers greater than 5 are included.

From the options provided:

• Option 1 has a closed point at 0.5 and goes left, which is incorrect.
• Option 2 has a closed point at 19.2 and goes right, which is also incorrect.
• Option 3 has a closed point at 5 but goes left, which is incorrect.
• Option 4 has a closed point at 5 and goes right, which is correct.

Therefore, the correct graph is Option 4.