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.

Draw the line make sure its dotted

Now pick a point NOT on the line

Find a position 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.

Shade it if its satisfied