```Question 284734

2x < 3y + 6

You want to solve for y so you can graph this equation.

first get all the y terms on the left side of the equation and everything else on the right side of the equation.

you do this in the following manner:

subtract 3y from both sides of the equation to get:

-3y + 2x < 6

subtract 2x from both sides of the equation to get:

-3y < -2x + 6

multiply both sides of the equation by -1 to get:

3y > 2x - 6

notice that the inequality is reversed when you multiply both sides of this equation by -1.

divide both sides of this equation by 3 to get:

y > (2/3)x - 2

graph the equality equation of y = (2/3)x - 2 to get:

{{{graph(400,400,-5,5,-5,5,(2/3)x-2)}}}

y will be any value above that line.

for example, when x = 3, any value of y > 0 will satisfy the equation.

to confirm, let x = 3 in your original equation.

2x < 3y + 6

when x is equal to 3, this becomes:

6 < 3y + 6

subtract 6 from both sides of this equation to get:

0 < 3y

divide both sides of this equation by 3 to get:

0 < y

since 0 < y is the same as y > 0, the solution is confirmed.

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