Question

How do I solve and graph this inequality?-2/3x + 2 < -4

Answer 1

The given inequality is:

`-(2)/(3)x+2<-4`

Subtract 2 from both sides

`\begin{gathered} -(2)/(3)x+2-2<-4-2 \\ -(2)/(3)x<-6 \end{gathered}`

Multiply both sides by 3

`\begin{gathered} 3(-(2)/(3)x)<3(-6) \\ -2x<-18 \end{gathered}`

Divide both sides by 2

`\begin{gathered} -(2x)/(2)<-(18)/(2) \\ -x<-9 \end{gathered}`

Multiply both sides by -1, and change the < symbol to >

`\begin{gathered} -1(-x)>-1(-9) \\ x>9 \end{gathered}`

The solution to the given inequality is:

x > 9

The graph of the solution x > 9 is shown below