Solving Two-Step Equations

1
Solving Two-Step Equations

• SPI 0606.3.6 Solve 2-step linear equations

2
What to Write

• Whenever you see this symbol, you need to copy
  the slide to your notes.

3
ONE STEP EQUATIONSLets Review!!!
4
One-Step Equations

• You only need to complete ONE STEP to solve the
  equation!

Wait a minute! Yesterday you said x equals 2!
X 2 5 X 3
5
ONE STEP EQUATIONS
An equation is like a balance scale because it
shows that two quantities are equal.
What you do to one side of the equation must also
be done to the other side to keep it balanced.
6
ONE STEP EQUATIONS
To solve one step equations, you need to ask
three questions about the equation

• What is the variable?

• What operation is performed on the variable?

• What is the inverse operation?

(The one that will undo what is being done to
the variable)
7
Procedure

• Isolate the variable by performing the inverse
  operation on that variable.
• The inverse of subtraction is adding. The
  inverse of adding is subtracting.
• The inverse of multiplication is division. The
  inverse of division is multiplication.
• Perform the same operation on the side of the
  equal sign that does not have a variable.

8
Example
We want to get the y by itself. Perform the
inverse operation. The inverse of adding is
subtracting.
y 13 25
- 13
- 13
Do the same operation on the other side of the
equal sign.
y 12
9
Check the answer in the original equation.
y 13 25
12 13 25
25 25
10
Example 2
To get k by itself, we perform the inverse
operation. The opposite of minus 12 is plus
12.
k 12 4
12
12
k 16
11
Check
k 12 4
16 12 4
4 4
12
Solving Multiplication and Division Equations
13
One Step-Multiplication Equation

• Example 3 Solve 6a 12

What is the variable?
The variable is a.
What operation is being performed on the variable?
Multiplication.
What is the inverse operation (the one that will
undo what is being done to the variable)?
Division
6a 12
6
6
a

2
14
One-Step Division Equation

• Example 4 Solve

10
What is the variable?
The variable is b.
What operation is being performed on the variable?
Division.
What is the inverse operation (the one that will
undo what is being done to the variable)?
Multiplication.
10
10
2
2
b

20
15
Practice Problems
Please take a few moments to complete the
following practice problems in your notes.
2x 18 10x 70 x/2 100 x/5 12
16
Solving 2-Step Variable EquationsLets Review
!!!!!
17
What??? I just reviewed 1-step!

• Relax. Youll use what you already know to solve
  2-step equations.

18
So, whats first?

• You need to break up the equation into its two
  steps.

19
STEP 1

• The first step will always be either adding or
• subtracting.

-
20
STEP 2

• The second step will always be either
• multiplying or dividing.

21
Lets try a problem
8x 5 61
22

• 8x 5 61

- 5
- 5
This problem has addition, so we need to subtract
first.
Whatever we do on one side, we have to do on the
other.
56

8x
23
Now, Step 2.

• 8x 56

Whatever we do on one side, we have to do on the
other.
This problem has multiplication, so we need to
divide now.
8
8
x
7

24
Lets try another problem

• 3a - 8 4

25

• 3a - 8 4

Whatever we do on one side, we have to do on the
other.
This problem has subtraction, so we need to add
first.
8
8
12

3a
26
Now, Step 2.

• 3a 12

Whatever we do on one side, we have to do on the
other.
This problem has multiplication, so we need to
divide now.
3
3
a
4

27
To Sum it all up !

• 2x 4 14

2x 4 14 - 4 - 4
1. Subtract 4 from both sides
2x 10 2 2
2. Divide both sides by 2
X 5
28
Now you try some problems

• DO NOW!

12t 6 90
7f 5 40
5q 7 13
4y 8 32