Solving Equations

Goal:

1.Get the variable alone.

2.Use Inverse Operations* to isolate the variable.

* - Inverse operations are opposite operations that undo each other. Addition and subtraction are inverse operations. Multiplication and division are inverse operations.

128xYou want to get the variable alone.

The “– 8 “ is standing in the way.

The Inverse Operation of “– 8 “ is “+8”, so we add 8 to both sides.

8 8

20xAlways check your work by inserting your answer back into the problem.

12820 If this is true, you KNOW you are right!

#1

1442 xYou want to get the variable alone.

The 2 and “+4 “ are standing in the way.

Work backwards through Order of Ops. Start by subtracting 4.

4 4

102 xAlways check your work by inserting your answer back into the problem.

5x

Now finish by doing the “Inverse Operation”.

2 2144)5(2

#2

832 x This is the TOUGH ONE!! 23 23

16

6

3

2

2

3

Notice how multiplying by a reciprocal eliminates the fraction!

Don’t be intimidated, we still perform the INVERSE OPERATION.

#3

832 x We do the same to the other side. 23 23

122

24

2

3

1

8

Equations always need to stay balanced.

#3

8)12(32 Always check your work!

81

12

3

2 8

3

24

88

#3

a) Before you leave class, take out a ½ sheet of paper.

b) Put your name and class period on it.

c) Answer these questions.

Questions

1. What is your goal when working an equation? (Look in your notes)

2. Define Inverse Operations. (Um…notes!?!)

3. Solve this equation and check your work to prove you are right.

1231 y