Question

solve the inequality and graph the solution.
$4 + 2y \geq 8$
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.
-5 -4 -3 -2 -1 0 1 2 3 4 5
submit

Explanation:

Step1: Subtract 4 from both sides

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

Step2: Divide by 2

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

To graph this solution:

• The endpoint is at \( y = 2 \). Since the inequality is "greater than or equal to", we use a closed dot at \( 2 \).
• Then we draw a ray to the right of \( 2 \) (towards positive infinity) to represent all values of \( y \) that are greater than or equal to \( 2 \).

Answer:

The solution to the inequality \( 4 + 2y \geq 8 \) is \( y \geq 2 \). The graph has a closed dot at \( 2 \) and a ray extending to the right from \( 2 \).