Question

solve:
-4<-3x+2<29

Answer 1

same way as if you were doing any other equation
keep in mind you want "x" isolated

so you'd need to get rid of the +2 first
then get rid of the -3

so you add and divide as needed

in this case you don't have a left-side and right-side
you have 3 sides, left, middle and rigth

any adding or subtracting or dividing, will have to occur to ALL 3 sides simultaneously

Answer 2

ok what would be the first step?

Answer 3

-4-2?

Answer 4

\(\bf -4<-3x+2<29\\
\textit{subtracting 2 from all 3 sides}\\
-4(-2)<-3x\cancel{+2(-2)}<29(-2) \implies -6 < -3x < 27\)

Answer 5

ok I understand. how do I get x by itself?

Answer 6

divide 3x all 3 sides?

Answer 7

got it

Answer 8

2<x<-9????

Answer 9

well, you want to leave the "x" by itself, so, you want to get rid of the -3

the one difference in simplifying inequalities, is that when dividing/multipliying/exponentializing by a NEGATIVE VALUE, you'd need to \(\bf \text{flip the sign}\)

Answer 10

that's correct, since you used -3, that is, NEGATIVE 3, then you'd need to flip the sign the other way

Answer 11

2<x>-9

Answer 12

??

Answer 13

do you agree

Answer 14

\(\bf -4<-3x+2<29\\
\textit{subtracting 2 from all 3 sides}\\
-4(-2)<-3x+2(-2)<29(-2) \implies -6 < -3x < 27\\
\textit{dividing by NEGATIVE 3}\\
2 \color{red}{>} x \color{red}{>} -9\)