Question

solve the inequality and graph the solution.

$9 < \frac{w}{-2} + 8$

to draw a ray, plot an endpoint and select an arrow. select an endpoint to
change it from closed to open. select the middle of the ray to delete it.

number line with -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5

submit

work it out
not feeling ready yet? these can help:
graph solutions to one-step inequ... (75)
solve multi-step inequalities
lesson: solving inequalities
lesson: inequalities on a number line

Explanation:

Step1: Subtract 8 from both sides

To isolate the term with \( w \), we subtract 8 from both sides of the inequality \( 9 < \frac{w}{-2} + 8 \).
\( 9 - 8 < \frac{w}{-2} + 8 - 8 \)
Simplifying both sides gives \( 1 < \frac{w}{-2} \).

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

When we multiply or divide an inequality by a negative number, we must reverse the inequality sign. So we multiply both sides of \( 1 < \frac{w}{-2} \) by -2.
\( 1\times(-2) > \frac{w}{-2}\times(-2) \)
Simplifying gives \( -2 > w \), or equivalently \( w < -2 \).

Answer:

The solution to the inequality is \( w < -2 \). To graph this, we plot an open circle at -2 (since the inequality is strict, \( w
eq -2 \)) and draw an arrow to the left (indicating all numbers less than -2).