Question

solve the inequality and graph the solution.
-5w + 3 ≥ 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.

Explanation:

Step1: Subtract 3 from both sides

$$-5w+3 - 3\geq8 - 3$$
$$-5w\geq5$$

Step2: Divide both sides by - 5 (reverse the inequality sign)

Since we divide by a negative number, the inequality sign flips.
$$\frac{-5w}{-5}\leq\frac{5}{-5}$$
$$w\leq - 1$$

Answer:

The solution of the inequality is \(w\leq - 1\). On the number - line, we plot a closed circle at \(w = - 1\) (because the inequality is \(\geq\) and after dividing by a negative we have \(\leq\), and the original inequality allows equality when \(w=-1\)) and draw a ray to the left.