6/05/2010 @ 8:12 PM

Equations

In this unit, you will learn about solving simple equations, multi-step equations, equations with fractions, and modeling with algebra/formulas.Simple equations are usually straightforward, and not very hard.

*TIP: Equations and expressions are NOT alike!*

*Expression: a*

*²b*

*² + 3ab -1*

*Equation: x*

*² - 3xy = 2*

*Equations have*

__equal__signs!

To "solve" means to find the value of the variables that makes the equation true. There are 2 ways of doing this, and the first way is solving by inspection.

Basically, what you do is solve for the missing variable- you can even eyeball the answer! (Eyeball- just look over and guess what the answer is- common sense)

EXAMPLE: x + 12 = 19

x = 7

The second way of solving an equation is solving by isolation. This is the way most people take, since it lets you check your answers with a LS/RS check.

What you do is isolate the variable on one side of the equation by using opposite operations.

EXAMPLE: y + 12 = 23

y= 23 - 12

y= 11

*TIP: Remember to do LS = RS check! For example:*y + 12 = 23, y = 11

**SAMDEB**

SAMDEB is actually BEDMAS backwards! Since we use opposite operations while solving equations, we use SAMDEB instead.

To use it, you first get rid of the constant term on the same side of variable with subtraction/addition, then you isolate the variable by multiplying/dividing the coefficient.

We also learned how to solve multi-step equations. These equations usually have more than one variable, usually 2. What you do is collect the variable terms on one side, and the constant terms on the other side.

EXAMPLE: 13x – 5 = 10x + 7

13x - 10x = 7 + 5

3x = 12

3x/3 = 12/3

x = 4

QUESTIONS:

Solve each equation:

1) x + 6 = 2x – 8

ANSWER: 6 + 8 = 2x -x

14 = x

2) 4(x – 2) = 12

ANSWER: 4x -8 = 12

4x = 12 + 8

4x = 20

4x/4 = 20/4

x = 5

3) 6(2x – 5) = 4x + 2

ANSWER: 12x - 30 = 4x + 2

12x - 4x = 2 + 30

8x = 32

8x/8 = 32/8

x = 4

Labels: Lessons

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