# Solving Two-Step Inequalities 03:05 minutes

**Video Transcript**

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Transcript
**Solving Two-Step Inequalities**

Miss Crazycat is sitting in her living room reading a letter she received from the City Council today. She is shocked! There is a new law: a maximum of 10 cats are allowed per household.

Miss Crazycat doesn't even know how many cats she has... and it's not exactly easy to count them as they are running around all the time.

But she does know how many cans of fish they eat. So she wants to use math by **solving two-step inequalities**.

### Example of a two-step Inequality

All her cats together eat 50 cans of fish in 5 days. Every cat eats at least one can of fish per day. We are looking for Miss Crazycat's total number of cats.

Since you don't know the number of cats yet let's call it x. But wait, Miss Crazycat just remembered, two of her cats are vegetarian. So the number of fish-eating cats is x - 2.

Let's summarize what we know. The fish-eating cats can be represented as x - 2. In 5 days they eat 50 cans of fish. Since Miss Crazycat knows that each cat eats at least one can of fish each day, you have to put a less than or equal to sign in between the two expressions.

### Solving a two-step Inequality

So let's calculate. We start with the **Distributive Property** here to eliminate the **paratheses**. You multiply x by 5 which is 5 x, and you multiply negative 2 by 5, which equals negative 10.

Now you use **opposite operations** to isolate your unknown number x. Remember to do this with **PEMDAS** reversed. The opposite of subtraction is addition, so we add 10 to the left side of the equation. What we do to one side, we must do to the other side: We add another 10 to the right side: 5x − 10 + 10 = 5x.

And 50 + 10 = 60. Remember, the less than or equal to sign stays the same unless multiplying or dividing by a negative number.

The **opposite of multiplication is division**, so you divide both sides by 5. The final answer is x ≤ 12. So we have 2 vegetarian cats and 10 or less fish-eating cats.

### Solutions on a Number Line

Let's show all of the possible solutions using a **number line**. The total number of cats is 12 or less. So it should look like this.

But Miss Crazycat can't have a negative number of cats, so the least possible solution is 0. Now we also know that she has two vegetarian cats. She also has to have at least one fish-eating cat because somebody has to be eating the fish! So she has at least 3 cats but no more than 12.

Miss Crazycat can't be certain that she is obeying the City Council's 10 cat limit. So just to be sure, she disguises two of the cats.