Question

solve the inequality and graph the solution.
( 4 < \frac{b}{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.
(longleftarrow) (vert) (vert) (vert) (vert) (vert) (vert) (vert) (vert) (vert) (vert) (longrightarrow)
-10 -8 -6 -4 -2 0 2 4 6 8 10
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work it out
not feeling ready yet? these can help:

Explanation:

Step1: Subtract 8 from both sides

To isolate the term with \( b \), we subtract 8 from both sides of the inequality \( 4 < \frac{b}{2}+8 \).
\[
4 - 8<\frac{b}{2}+8 - 8
\]
Simplifying the left and right sides, we get:
\[

• 4<\frac{b}{2}

\]

Step2: Multiply both sides by 2

To solve for \( b \), we multiply both sides of the inequality \( - 4<\frac{b}{2} \) by 2.
\[
-4\times2<\frac{b}{2}\times2
\]
Simplifying both sides, we obtain:
\[
-8 < b
\]
Which can also be written as \( b>-8 \)

Answer:

The solution to the inequality is \( b > - 8 \). To graph this, we plot an open circle at \( - 8 \) (since the inequality is strict, \( b
eq - 8 \)) and draw an arrow to the right (indicating all values greater than \( - 8 \)).