Algebra Know-It-ALL

173

CHAPTER

11

Equations and Inequalities

You’ve learned how numbers and variables can be combined to form equations. Now it’s time

to get more adept with simple equations. You’ll also learn the basic principles of inequalities.

Equation Morphing Revisited

In Chap. 5, we mentioned some rules for manipulating equations. Let’s examine these rules in

more detail. Keep in mind that in any equation, there are two or more parts separated by one

or more equality symbols, also called equals signs. The most basic form of equation has a left

side and a right side, with a single equality symbol between them.

Changing the order

An equation can be stated in any order. If there are only two expressions with an equals sign

between them, we can reverse the right and left sides. If we see a=b, we can change it to b=a.

If there are more than two expressions, we can rearrange them however we want.

Adding or subtracting a quantity

All the parts of an equation have the same value, so we can add the same quantity to each part

and have those parts remain equal. Here’s a simple example with numbers:

5/2= 20/8

Both sides of this equation are equal to 2-1/2. If we add 7 to each side, we get

5/2+ 7 = 20/8 + 7

Simplifying each side of this gives us 9-1/2 = 9-1/2.

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