Question

solve the inequality and graph the solution.
18 < \\(\frac{m}{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)---(open circle at -4)---(-3)---(-2)---(-1)---(0)---(1)---(2)---(3)---(4)---(5)--->
submit

Explanation:

Step1: Subtract 20 from both sides

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

• 2<\frac{m}{2}

\]

Step2: Multiply both sides by 2

To solve for \( m \), we multiply both sides of the inequality \( - 2<\frac{m}{2} \) by 2.
\[
-2\times2<\frac{m}{2}\times2
\]
\[

• 4 < m

\]
Which can be rewritten as \( m>-4 \)

Answer:

The solution to the inequality is \( m > - 4 \). To graph this, we draw an open circle at \( - 4 \) (since the inequality is strict, \( m
eq - 4 \)) and draw a ray to the right of \( - 4 \) on the number line.