Question

solve the inequality and graph the solution. (\frac{k}{3}-19 > - 18). 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 k

Add 19 to both sides of the inequality $\frac{k}{3}-19 > - 18$.
$\frac{k}{3}-19 + 19> - 18+19$
$\frac{k}{3}>1$

Step2: Solve for k

Multiply both sides of the inequality by 3.
$3\times\frac{k}{3}>1\times3$
$k > 3$

To graph the solution:

1. Draw a number - line.
2. Mark a point at 3. Since the inequality is $k>3$ (strict inequality), use an open - circle at 3.
3. Shade the number - line to the right of 3 to represent all the values of k that satisfy the inequality.

Answer:

$k > 3$; Graph: Open - circle at 3, shade to the right on the number - line.