One and Two Step One and Two Step EquationsEquations

Using Opposite OperationsUsing Opposite Operations

When working to get the variable isolated and all alone, use the opposites rule.

Opposites Rule – to get rid of a term from either side of an equation, just do the opposite operation.

1. C + 3 = 5

Variab

le

Mark the variable then leave it alone. Move everythingaway from the variable.

- 3 - 3

C = 2

2. m - 3 = 5+3

= 8

+3

m

Variab

le

3. P + (-12) = -5

“fix” double signs first

P – 12 = -5+12 +12

P = 7

4. Y - (-6) = 3 Y + 6 = 3

- 6 -6

Y = -3

“fix” double signs first

5. X + 2.2 = 9.2- 2.2

X = 7

- 2.2

6. X – (-28) = - 48 X + 28 = - 48

- 28

- 28

X = - 76

7. 9x = 45This reads 9 times xSo use the opposite.

Divide both sides by 9.9 9

x = 5

8. - 4m = - 28

- 4 - 4

m = 7

68

k

This is a division

Problem, use

Multiplication

to solve it.

9.

- k

(8) (8)

= 48 Now Divide By -1 - 1 - 1

k = - 48

10. 115

x

(-5) (-5)

= x 55

Let’s try a problem.Let’s try a problem.

8x + 5 = 618x + 5 = 61This problem has addition, so we need to subtract first.

- 5 - 5 Whatever we do on one side, we have to do on the other.

8x 56=

Now, Step 2.Now, Step 2.

8x = 568x = 56This problem has multiplication, so we need to divide now.

Whatever we do on one side, we have to do on the other.8 8

x = 7

Let’s try another problem.Let’s try another problem.

3a - 8 = 43a - 8 = 4This problem has subtraction, so we need to add first.

+ 8 + 8 Whatever we do on one side, we have to do on the other.

3a 12=

Now, Step 2.Now, Step 2.

3a = 123a = 12This problem has multiplication, so we need to divide now.

Whatever we do on one side, we have to do on the other.3 3

a = 4

Let’s try another problem.Let’s try another problem.

zz + 2 = 26 + 2 = 26 66This problem has addition, so we need to subtract first. - 2 - 2

Whatever we do on one side, we have to do on the other.

24=z6

Now, Step 2.Now, Step 2.

This problem has division, so we need to multiply now.

Whatever we do on one side, we have to do on the other.

z = 144

z = 246

6 • • 6

Let’s try one more problem.Let’s try one more problem.

mm - 10 = 15 - 10 = 15 55This problem has subtraction, so we need to add first. +10 +10

Whatever we do on one side, we have to do on the other.

25=m5

Now, Step 2.Now, Step 2.

This problem has division, so we need to multiply now.

Whatever we do on one side, we have to do on the other.

m = 125

m = 255

5 • • 5