Question

solve the inequality and graph the solution. -3b + 9 ≥ 3 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. submit

Explanation:

Step1: Subtract 9 from both sides

$$\begin{align*} -3b+9 - 9&\geq3 - 9\\ -3b&\geq - 6 \end{align*}$$

Step2: Divide both sides by -3 and reverse the inequality sign

When dividing an inequality by a negative number, the inequality sign flips.

$$\begin{align*} \frac{-3b}{-3}&\leq\frac{-6}{-3}\\ b&\leq2 \end{align*}$$

Answer:

The solution of the inequality is \(b\leq2\). On the number - line, we plot a closed circle at \(2\) (because the inequality includes equality, i.e., \(b = 2\) is part of the solution) and draw a ray to the left of \(2\) (since \(b\) can be any number less than or equal to \(2\)).