Solving One-Step Inequalities by Multiplying or Dividing 03:36 minutes

Video Transcript

Transcript Solving One-Step Inequalities by Multiplying or Dividing

To learn how to solve one-step inequalities with multiplication and division, let’s go back in time.

Look! Two cavemen are eating dinner. Seems like they're just about finished! Look at all those bones!

One of the cavemen picks up a bone and throws it. He hits a rock. What fun! The cavemen decide to make a game of it and throw the bones for points. First, they agree on the rules.

One-Step Inequality Example Calculation 1

Each hit on the bullseye is worth 3 points and a loss of half of a point for each miss. This caveman has 12 Points. Since we don't know the number of times he hit the bullseye, we'll let the variable x represent this quantity.

Each time the cavemen hit the bullseye is worth 3 points. If there were no misses, 3x would equal 12. But since we know that every miss costs the cavement precious points. So it's possible that the cavemen missed the target on a few throws.

Let's write an inequality: 3x ≥ 12.

To solve the inequality, divide each side by 3: x ≥ 4. To have a score of 12, the caveman could have hit the bullseye 4 or more times.

One-Step Inequality Example Calculation 2

Here's the second contender. Oh man! The second caveman's score is minus 11 points.

If the second caveman didn't hit the target a single time, negative 1/2 x would equal minus 11, where x is the number of throws. But his total number of throws might be higher if he was successful at hitting the target on occassion. So, −1/2 · x ≤ −11.

To solve the inequality, divide both sides by negative one-half which is the same as multiplying both sides by the inverse of negative one-half which is negative two.

Since you are multiplying or dividing by a negative number, don’t forget you have to flip the inequality sign.

x is greater than or equal to 22. He could have made 22 or more attempts! This caveman is a persistent fellow! He should get extra credit for effort!

Why flip the Inequality Sign?

But when we multiply or divide with a negative number, why do we flip the inequality? To flip or not to flip, that is the question.

Let's look at another example. Negative two is less than five. Watch what happens when we divide both sides by negative 1, but this time, we won't flip the inequality. −2 ÷ −1 < 5 ÷ −1. So we get 2 < −5!

2 < −5? That’s not right. But, if we flip the sign, like we were supposed to, then we get a true inequality. So remember:

When you multiply or divide an inequality by a negative number, you must flip the inequality sign.

There they go again! They're really persistent! Hooray, he got one! He hit the bullseye! Oh no! That's not a rock! Run cavemen! Run!

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