Question

solve the inequality and graph the solution.
\\(\frac{w}{-1} + 8 < 4\\)
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.
\\(longleftarrowquad -5quad -4quad -3quad -2quad -1quad 0quad 1quad 2quad 3quad 4quad 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 \(\frac{w}{-1}+8 < 4\).
\[
\frac{w}{-1}+8 - 8<4 - 8
\]
Simplifying both sides, we get:
\[
\frac{w}{-1}<-4
\]

Step2: Multiply both sides by -1 (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 \(\frac{w}{-1}<-4\) by -1.
\[
w>(-4)\times(-1)
\]
Simplifying the right - hand side, we have:
\[
w > 4
\]

Answer:

The solution to the inequality is \( w>4 \). To graph this, we plot an open circle at 4 (since the inequality is strict, \( w
eq4 \)) and draw an arrow to the right (indicating all values greater than 4).