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Solving Inequalities Using Multiplication Or Division

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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 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:

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

Solving Inequalities Using Multiplication or Division

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.