Question

solve the inequality and graph the solution.
2r + 10 ≥ 2
to draw a ray, plot an endpoint and select an arrow. select an endpoint to change it from closed to open. select the middle of the ray to delete it.
-5 -4 -3 -2 -1 0 1 2 3 4 5

Explanation:

Step1: Subtract 10 from both sides

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

Step2: Divide both sides by 2

Next, we divide both sides of the inequality \( 2r \geq -8 \) by 2 to solve for \( r \). So, \( \frac{2r}{2} \geq \frac{-8}{2} \), which simplifies to \( r \geq -4 \).

Step3: Graph the solution

The solution \( r \geq -4 \) means we plot a closed dot at \( -4 \) (since the inequality is "greater than or equal to") and draw an arrow to the right (indicating all numbers greater than or equal to \( -4 \)).

Answer:

The solution to the inequality is \( r \geq -4 \), and the graph has a closed endpoint at \( -4 \) with an arrow pointing to the right.