Question

solve the inequality and graph the solution. 8 + \frac{y}{4} \leq 9. 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: Isolate the variable y

Subtract 8 from both sides of the inequality $8+\frac{y}{4}\geq9$.
$8+\frac{y}{4}-8\geq9 - 8$
$\frac{y}{4}\geq1$

Step2: Solve for y

Multiply both sides of the inequality by 4.
$4\times\frac{y}{4}\geq4\times1$
$y\geq4$

To graph the solution on a number - line:

1. Plot a closed circle at $y = 4$ (because the inequality is $\geq$, so 4 is included in the solution set).
2. Draw a ray to the right of 4 to represent all the values of y that are greater than or equal to 4.

Answer:

The solution of the inequality is $y\geq4$. On the number - line, plot a closed circle at 4 and draw a ray to the right.