Question

solve the inequality and graph the solution.
10 + 4r ≥ 2
plot the endpoints. select an endpoint to change it from closed to open. select the middle of the segment, ray, or line to delete it.

Explanation:

Step1: Subtract 10 from both sides

To isolate the term with \( r \), we subtract 10 from both sides of the inequality \( 10 + 4r \geq 2 \). This gives us \( 10 + 4r - 10 \geq 2 - 10 \), which simplifies to \( 4r \geq -8 \).

Step2: Divide both sides by 4

To solve for \( r \), we divide both sides of the inequality \( 4r \geq -8 \) by 4. Since 4 is a positive number, the direction of the inequality sign remains the same. So we have \( \frac{4r}{4} \geq \frac{-8}{4} \), which simplifies to \( r \geq -2 \).

Answer:

The solution to the inequality \( 10 + 4r \geq 2 \) is \( r \geq -2 \). To graph this, we plot a closed dot at \( -2 \) (because the inequality is "greater than or equal to") and draw a ray to the right of \( -2 \) on the number line.