how do you turn an inequality to an equation?

Question

for example:

1/2x < -y

x<2

3x+ 2y>-3

Answer 1

You don't really turn it into an equation, you solve the associated equation and then choose the solution to the inequality in terms of that.
In your examples you have two values, x and y, which will graph to a straight line. Then the solution to the inequality will be the half-plane on one side of the line.
For example, with 1/2 x < -y, the associated equation is
1/2 x = -y or -1/2x = y
Graph this and you'll get a line thru the origin and including points such as (2, -1) and (-2, 1)
Now you need to choose one side or the other of the plane which satisfies the inequality. Just pick a point (any point) on either side of the line (not lying on the line) and plug it into the inequality and see if it's true. If so, then the entire half plane that includes that point will be the solution. If not, you want the other half plane, on the other side of the line.
I like to use the origin when possilbe, but not possible here because it's on the line. So I'll look at the graph and choose any point whose coordinates are easy numbers to work with, and which clearly lies on one side of the line or the other. Let's say (4,8)
(1/2)x 4 = 2 > -8 so you want the half plane on the opposite side of the line, which does not include the point (4,8)
You'd do the others the same way.
Just replace the inequality sign with an equal sign, and graph the equation.
x = 2 (this will give you a vertical line with no y intercept)
3x + 2y = -3 (this will give you a slant line with x and y intercepts)
Then choose a point -not- on the line, see if it works in the original inequality. If it does, that half-plane is your solution. If it doesn't, then the other half-plane is your solution.
Since these are all strict inequalities, (that is, they are > or < rather than >= or <=), your solution will NOT include the line which forms the boundary between the half planes.

Answer 2

1) 1/2x < -y
You devide both sides by -1 to get
y>-1/2x ( you flip the sign when you multiply by a negative number.)
If your graphing this, you graph the line y = -1/2x. Then you have to decide when y is greater than -1/2x. When y is 0, X = 0. When y < 0, x > 0. So y > -1/2x when y > 0. Try drawing the graph to see what it looks like.
2) x < 2
This is where x is less than 2. Imagine the graph x = 2 and this represents everything to the left of that line.
3) 3x + 2y > 3
2y > 3 - 3x
y > 3/2 - 3/2x
Graph this and look when y is greater than 3/2 - 3/2x.
You can't turn an inequality into an equation, because they represent different things. X < 2 does not mean x = 2. You can though, figure out what the inequality describes. Sometimes just by algebra, but a graph always helps.

Answer 3

just replace < or > with =

that will give you the equation of the line that separates area where the inequality holds from the one where it isn't. Check one point (like origin or (1,1) to see which is which.

Answer 4

You replace the inequality symbol (i.e. < or >) with an equals sign. This will change the possible answers from usually infinate to one.