Two-step inequalities are called like that because we need to perform two steps to find the solution. They come in form:
First step in solving them is the same as the one in one step inequalities. So the b goes to the other side, becomes negative self:
Since the x is the value we are looking for, there is still something in the way. a multiplies x, so we have to deal with that before we can have our x.
Here is where you have to be careful. We have to divide our whole inequality with that a, but an inequality sign depends on whether it is negative or positive.
Let’s try it on a few examples:
(, so the inequality sign remains the same)
On the number line (again, since it is strictly lesser, number two isn’t included in the solution set):
In this case x is multiplied by (-7) so we should divide it by (-7), but it is a negative number, so the inequality will change from to .
Here we have that x is greater or equal than 1. That means that x will be included in the solution set.
It would have been similar if the task was set like this:
(we divide by a negative number
so the inequality changes from )
And in the form of an interval: .
Two-step inequalities worksheets
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