One and Two Step Equations Using Opposite Operations.

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