Posted by Casey on Tuesday, February 12, 2013 at 2:58pm.
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?

Algebra  Steve, Tuesday, February 12, 2013 at 4:16pm
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
3x6 > 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.
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