Question 284734
your equation is:


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.


your original equation is:


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.