how do you do this?

Question

2x + 3y < 2; (5,2) (2,-1) ?? How do you do that I dont know how to,

Answer 1

Do what? Decide if those points are part of the solution set? If so, plug them into the inequality and see if it turns out to be true:

2(5) + 3(2) < 2
10 + 6 < 2
16 < 2
not true, so (5,2) not in solution set.

2(2) + 3(-1) < 2
4 - 3 < 2
1 < 2
true, so (2,-1) is in solution set.

Answer 2

The way the question is put leaves a vague idea of what is asked, however we can go ahead and analyze what we can.

The two points may be test points and we simply plug them in to the inequality and see if the inequality
holds true or not.

The first one is
2*(5)+ 3*(2) = 10+15 = 25<2 is false
2*x+3*y<2 does not contain (5,2) in the answer set

Another way to do this is solve for either x, or y
y<2*(1-x)/3
substitute a value for x.
y<2*(-5)/3
y<-10/3 when x=5
this gives us every y that can casisfy the inequality (at x=5).
since 2 is not less than -3.3333 then (5,2) does not satisfy the inequality.

if you graph y=2*(1-x)/3
you get a line and every point under the line is a solution. Get the picture?

when solving inequalities, if you have to divide or multiply both sides by a negative number, the inequality reverses
if x>0 then -x<0

Hope this helps.
~steve~