Caddell Prep Access Menu

Solving Inequalities Using Multiplication or Division

In this video, we will be learning how to solve inequalities using multiplication or division.

For Example:

-3x\leq-15

\frac{-3x}{-3}\leq\frac{-15}{-3}\leftarrow Divide by -3 on both sides (Don’t forget to flip the inequality sign since we are dividing by a negative!)

x\geq5\leftarrow Graph the inequality

xgeq5

Video-Lesson Transcript

Let’s go over solving 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:

3x \leq 12

To solve for x, we have to divide both sides by 3.

\dfrac{3x}{3} \leq \dfrac{12}{3} x \leq 4

Next we have

-4x \leq 20

Let’s solve x by dividing both sides by -4

\dfrac{-4x}{-4} \leq \dfrac{20}{-4}

Since we divide it by a negative number, the inequality sign should be flipped.

x \geq -5

Let’s look at another example.

12x > -36

So, we’ll solve x by dividing both sides by 12.

\dfrac{12x}{12} > \dfrac{-36}{12}

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 12. So there’s no need to flip the sign.

So the answer is:

x > -3

Next, let’s have

\dfrac{x}{-5} \geq 40

To solve for x, let’s divide both sides by -5.

-5 \times \dfrac{x}{-5} \geq 40 \times{-5}

Here, we multiplied by a negative number so we have to flip the inequality sign.

So the answer is

x \leq -200

So in solving inequalities using multiplication or division, follow the same rules to solve for x.

But if we, at any point, multiply or divide by a negative number, we have to flip the inequality sign.