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### Inequalities

```
Date: 01/24/2001 at 22:08:56
From: Nick Kincannon
Subject: Pre-Algebra

How do you add, subtract, multiply, and divide inequalities?
```

```
Date: 01/26/2001 at 13:18:47
From: Doctor Alicia
Subject: Re: Pre-Algebra

Hi Nick,

When you add, subtract, multiply, and divide inequalities, you treat
the inequality as if it were an equation (=). You flip the inequality
if you divide or multiply by a negative number.

For example:

7 + 2x > 12

Subtract 7 from both sides:

7 - 7 + 2x > 12 - 7

2x > 5

Divide both sides by 2 but keep the inequality symbol as-is:

2x > 5
---  ---
2    2

x > 5
---
2

Therefore, x is greater than 5/2.  To check our work, pick any x
greater than 5/2, such as 7/2.

7 + 2 * 7 > 12
---
2

The 2's cancel out:
7 + 7 > 12

14 > 12

So we see that our inequality holds true.

Now, let's try the a similar problem but one dealing with multiplying
or dividing negative numbers:

7 - 2x > 12

Subtract 7 from both sides:

7 - 7 - 2x > 12 - 7

- 2x > 5

Divide by *negative* 2 and flip the inequality:

- 2x < 5
---  ---
- 2   -2

The -2's cancel out:

x < -5
---
2

Therefore, x is less than -5/2.  To check our work, pick a number less
than -5/2, such as -10.

7 - 2(-10) > 12

7 + 20 > 12

27 > 12

We see that the inequality holds true.

I hope this helps. Write back if you have any further questions.

- Doctor Alicia, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Algebra

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