Question

Solve the system of inequalities.

y<2x+4
-3x - 2y> 6

So I just want y alone. For the second inequality, I added 3x to both sides and got -2y> 3x+6. Then I divided both sides by -2. I got y> -3/2 - 3
Do I have to switch the inequality symbol or something?

Answer 1

whenever you multiply/divide by a negative value, the direction of the inequality changes. It's just a shorthand for moving things to the other side. For example,

-2x < 8
0 < 8+2x
-8 < 2x
-4 < x
or, just dividing by -2 and switching the direction,
x > -4

So, for your problem,

-3x - 2y> 6
-3x-6 > 2y
y < -3/2 x - 3

Also, we have
y < 2x+4

So, to satisfy both equations,
find where the two lines intersect. The solution set is points where y is below both lines.