Solving 2-Step Variable Equations

1
Solving 2-Step Variable Equations
2
Two Step Equations Essential Question

• How are inverse operations used to solve two step
  equations?
• Why does order matter when solving two step
  equations?

3
Solving Two-Step Equations

• To find the solution to an equation we must
  isolate the variable. In other words, get the
  variable on one side of the equation by itself.
• We isolate the variable by performing operations
  that will eliminate (cancel) the other numbers
  from the expression.

4
Solving Two-Step Equations

• We have seen how to eliminate a constant
  (Addition Property of Equality) how to
  eliminate a coefficient (Multiplication Property
  of Equality).
• What if an equation has both a constant and a
  coefficient to be eliminated?
• This is called a Two-Step Equation.

5
So, whats first?

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

6
STEP 1

• The first step will always be either adding or
• subtracting. (Think Order of Operations
  backwards)

-
7
STEP 2

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

8
Lets try a problem.

• 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
9
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

10
Lets try another problem.

• 3a - 8 4

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

3a
11
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

12
Lets try another problem.

• z 2 26
• 6

Whatever we do on one side, we have to do on the
other.
This problem has addition, so we need to subtract
first.
- 2
- 2
z 6

24
13
Now, Step 2.
z 24 6
6
6
Whatever we do on one side, we have to do on the
other.
This problem has division, so we need to multiply
now.
z
144

14
Lets try one more problem.

• m - 10 15
• 5

Whatever we do on one side, we have to do on the
other.
This problem has subtraction, so we need to add
first.
10
10
m 5

25
15
Now, Step 2.
5
m 25 5
5
Whatever we do on one side, we have to do on the
other.
This problem has division, so we need to multiply
now.
m
125

16
Examples of Two-Step Equations

1. 3x 5 16
2. y/4 3 12
3. 5n 4 6
4. n/2 6 4