You can put this solution on YOUR website! 2x<3y+6
Since y is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.
3y+6>2x
Since 6 does not contain the variable to solve for, move it to the right-hand side of the inequality by subtracting 6 from both sides.
3y>-6+2x
Move all terms not containing y to the right-hand side of the inequality.
3y>2x-6
Divide each term in the inequality by 3.
(3y)/(3)>(2x)/(3)-(6)/(3)
Simplify the left-hand side of the inequality by canceling the common factors.
y>(2x)/(3)-(6)/(3)
Simplify the right-hand side of the inequality by simplifying each term.
y>(2(x-3))/(3)
2x<3y+6
Divide each term in the inequality by 2.
(2x)/(2)<(3y)/(2)+(6)/(2)
Simplify the left-hand side of the inequality by canceling the common factors.
x<(3y)/(2)+(6)/(2)
Simplify the right-hand side of the inequality by simplifying each term.
x<(3(y+2))/(2)
Treat the < sign as an equals sign, and rearrange the equation so that it looks like the equation of a line, y=mx+b
2x<3y+6
Subtract 6 from both sides:
2x-6 < 3y
Now divide both sides by 3:
(2x-6)/3 < y
2x/3 - 6/3 < y
2x/3 -2 < y
So comparing it to the equation of a line, this tells us that the slope is m=2/3 and the y-intercept is b=-2.
You can plot this on a graph by plotting the line of y=2x/3 -2, and then shading in the area underneath the line (because we were saying the inequality was showing everything that is less than y).
Here's a link to Wolfram Alpha's graph of it: http://www.wolframalpha.com/input/?i=2x-6+%3C+3y
