Inequalities and graphs example 3

Solve the inequality

`6x-y>\-2` 

Subtract `6x` from both sides to get `y` on its own.

`6x-6x-y>\-2-6x`

`-y>\-2-6x` 

Divide both sides by `-1`  to get a positive. Don’t forget to FLIP the sign.

`(-y)/\-1<-(2x)/-1-(6x)/-1`

`y<\2+6x` 

or `y<\6x+2` 

First let's calculate points on the graph

`x=-2`       then   `y<\6(-2)+2=-12+2=-10`

`x=-1`       then   `y<\6(-1)+2=-6+2=-4`     

`x=0`             then   `y<\6(0)+2=0+2=2`      

`x=1`             then   `y<\6times1+2=6+2=8`         

`x=2`             then   `y<\6times2+2=12+2=14`     

Now draw a graph and mark on the above points. Don’t forget to use a DOTTED line.

Now pick a point NOT on the line

Choose   `x=0`   `y=0`

`y<\6x+2` 

`0<\6(0)+2` 

`0<\2`  

This reads zero is less than two.

This does satisfy the inequality, SHADE IT.