Solving Inequalities Examples

Solve for y:

Here you can choose which side of the inequality to get the variables on. It's really up to you and whatever way makes more sense. In this problem, we'll move the variables to the left side.

	add y to each side
	remember y is the same as 1y
	subtract 2 from each side
	simplify
	divide each side by 4
or	notice that the sign didn't switch

Since we divided each side by positive 4, we don't need to switch the > to <.

To check, we need to pick a number greater than 2.5 and plug it into the original inequality. Let's try 4.

Well, 14 is greater than 4, so we're all good!

Solve for x:

Just like with equations, we need to get the variable out of the denominator. We start by multiplying each side by (2x – 1).

	multiply each side by (2x – 1)
	the (2x – 1)'s on the left cancel
	distribute the -2
	subtract 2 from each side
	simplify
	divide each side by -4
	switch the sign from ≥ to ≤

Since we divided each side by negative 4, we switched the sign from ≥ to ≤.

To check, plug in any number greater than or equal to -½. Since it can equal -½, let's plug that in.

-2 is greater than or equal to -2!

Solve for z:

First multiply each side by -3.

	multiply each side by -3
	switch the sign since we multiplied by -3
	subtract 2 from each side
	simplify

We switched the sign in the second step because we multiplied by a negative number.

We got z ≥ -20, so check by plugging in any number ≥ -20, like 0.

Yup, -⅔ is smaller than 6!