Question

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

Answer 1

The given inequality is:

$-\frac{2}{3}x+2<-4$

Subtract 2 from both sides

$\begin{gathered} -\frac{2}{3}x+2-2<-4-2 \\ -\frac{2}{3}x<-6 \end{gathered}$

Multiply both sides by 3

$\begin{gathered} 3(-\frac{2}{3}x)<3(-6) \\ -2x<-18 \end{gathered}$

Divide both sides by 2

$\begin{gathered} -\frac{2x}{2}<-\frac{18}{2} \\ -x<-9 \end{gathered}$

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