In this video, we will be learning how to solve inequalities using multiplication or division. After you finish this lesson, view all of our Algebra 1 lessons and practice problems.
Example of Solving an Inequality Using Multiplication/Division
Divide by -3 on both sides (Don’t forget to flip the inequality sign since we are dividing by a negative!)
Example 1
To solve for , we have to divide both sides by
Then, graph the inqequality
Example 2
To solve for , let’s multiply both sides by
Then, graph the inqequality
Video-Lesson Transcript
Let’s go over how to solve inequalities using multiplication or division
The rules are very similar to solving regular equations except for one rule.
If we multiply or divide by a negative number, we have to flip inequality.
Here are some examples:
To solve for , we have to divide both sides by .
Next we have
Let’s solve by dividing both sides by
Since we divide it by a negative number, the inequality sign should be flipped.
Let’s look at another example.
So, we’ll solve by dividing both sides by .
Here, its negative divided by positive.
Remember the rule? If we multiply or divide by a negative number, we have to flip inequality.
In this example, we are dividing by positive . So there’s no need to flip the sign.
So the answer is:
Next, let’s have
To solve for , let’s divide both sides by .
Here, we multiplied by a negative number so we have to flip the inequality sign.
So the answer is
So in solving inequalities using multiplication or division, follow the same rules to solve for .
But if we, at any point, multiply or divide by a negative number, we have to flip the inequality sign.