Question

solve the inequality and graph the solution.
7 + 3r ≥ 4
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 term with the variable

Subtract 7 from both sides of the inequality $7 + 3r\geq4$.
$7+3r - 7\geq4 - 7$
$3r\geq - 3$

Step2: Solve for r

Divide both sides of the inequality by 3.
$\frac{3r}{3}\geq\frac{-3}{3}$
$r\geq - 1$

To graph the solution:

• The endpoint of the solution set is $r=-1$. Since the inequality is $\geq$, the endpoint at $r = - 1$ is a closed - circle.
• The solution set includes all values of $r$ greater than or equal to - 1, so we draw a ray starting at $r=-1$ and going to the right.

Answer:

The solution of the inequality is $r\geq - 1$. On the number - line, there is a closed - circle at $r=-1$ and a ray extending to the right.