Question

please show me the correct steps for this absolute value inequality: 4−3|m+2|>−14

Answer 1

first you to isolate the variables on one side and the numbers on the other...

add -4 to both sides: -3|m-2|>-18
then you want to get that pesky -3 out of the way by dividing through by -3 (don't forget to switch the inequality when dividing a negative)
|m-2|<6
then you can add through by the 2
m<6

Answer 2

i think that is correct, but i DID just do it in my head so please recheck the numbers, but the logic is there :)

Answer 3

There has to be 2 solutions

Answer 4

HAHAHAH oops
its not lol i can't add the last step i think....
m<6+2 so
m<8

Answer 5

You changed m+2 to m-2

Answer 6

oh ok i copied it wrong.... but you can figure it out from there though right?

Answer 7

\(\bf 4−3|m+2|>-14 \implies -3|m+2|>-10\\
\textit{when dividing/multiplying/exponentializing by a negative value}\\
\textit{don't forget to } \color{red}{\text{flip}} \textit{ the inequality sign}\\
-3|m+2|>-10 \implies |m+2| < \cfrac{-10}{-3} \implies
\begin{cases}
+1(m+2) < \cfrac{-10}{-3}\\\quad \\
\bf -1(m+2) < \cfrac{-10}{-3}
\end{cases}\)

Answer 8

hmmm.. shouldn't be -10... one sec

Answer 9

ohh nevermind, yes it should

Answer 10

acckk.. hold on, rats

Answer 11

\(\bf 4-3|m+2|>-14 \implies -3|m+2|>-18\\
\textit{when dividing/multiplying/exponentializing by a negative value}\\
\textit{don't forget to } \text{flip} \textit{ the inequality sign}\\
-3|m+2|>-18 \implies |m+2| < \cfrac{-18}{-3} \implies
\begin{cases}
+1(m+2) < \cfrac{-18}{-3}\\\quad \\
\bf -1(m+2) < \cfrac{-18}{-3}
\end{cases}\)

Answer 12

Well actually I know that the solution is -8<m<4, but I just want to know the steps. The steps are the only thing that are keeping me from getting those solutions.