Question

solve the inequality and graph the solution.
$18 \geq \frac{u}{-2} + 20$
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.
-5 -4 -3 -2 -1 0 1 2 3 4 5

Explanation:

Step1: Subtract 20 from both sides

To isolate the term with \( u \), we subtract 20 from both sides of the inequality \( 18 \geq \frac{u}{-2}+20 \).

$$ 18 - 20\geq\frac{u}{-2}+20 - 20 $$

$$ - 2\geq\frac{u}{-2} $$

Step2: Multiply both sides by -2 (and reverse inequality)

When multiplying or dividing an inequality by a negative number, the direction of the inequality sign changes. We multiply both sides by -2.

$$ (-2)\times(-2)\leq\frac{u}{-2}\times(-2) $$

$$ 4\leq u $$

Which can be rewritten as \( u\geq4 \)

Answer:

The solution to the inequality is \( u\geq4 \). To graph this, we plot a closed dot at 4 (since the inequality is "greater than or equal to") and draw a ray to the right of 4 on the number line.