Equations - Opposite Operations

It is important to learn this process, so that

you can apply it to more difficult equations!

Solving Two-Step Equations

left hand side

Every equation has 2 sides, separated

by the = sign.

4 + x

=
12
right hand side
The opposite of multiplication is division.
The opposite of division is multiplication.
The opposite of subtraction is addition.

The opposite of addition is subtraction.

We also use OPPOSITE OPERATIONS
to get the pro-numeral by itself.
Example  1

The opposite of addition is subtraction, so we need

to subtract 9 from both sides of the equation.

We need to UNDO the 9, which is added to p.

+  9  =  12
p
-
9
=
- 9
3

You must show

the steps of

solving your

equations in

this manner!

Example  2

We need to UNDO the 3, which is subtracted from s.

The opposite of subtraction is addition, so we need

to add 3 to both sides of the equation.

s

 -  3  =  17

+

3

=
+ 3

20

You must show

the steps of

solving your

equations!

Example  3

The opposite of multiplication is division, so we need

to divide both sides of the equation by 5.

We need to UNDO the 5, which is multiplied by x.

÷

 5x    =     35

x

5

=

÷  5

7

You must show

the steps of

solving your

equations!

We use this same process when more than

one number is on the same side of the

equation as the variable.

However, it is important to remember to use

opposite operations to

 

undo ADDITION or SUBTRACTION BEFORE

undoing MULTIPLICATION or DIVISION.

 

 (Remove the seperate value first)

Example 1
4
x
 ÷4          ÷4
4x      =  12
+
x
-   9
9
=
=
- 9
21
3
solution
divide both sides by 4
subtract 9 from both sides
Example 2
2p  -  3  =  27
2p         =   30
÷2
p      =  15
+ 3
+3
 ÷2
add 3 to both sides
solution
divide both sides by 2
What is the first step in solving this equation?
6a   -  3   =  21

 add 6

 add 3

 subtract 6

 subtract 3

Identify the next step in solving this equation.
4b  +  8  =  56
4 +  0  =  48
4b      =  48
-  8

 add 4 to both sides

 multiply both sides by 4

 divide both sides by 4

 subtract  4 from both sides

-8
Your turn!
5y   -  15    =  20
Fill in the missing numbers.
÷
5y     =    35
y    =
​÷
Solve.
3y  +  8    =  23
​÷
3y     =    15
y    =
​÷
Solve.
6y   +  7    =  37
​÷
6y     =    30
y    =
​÷
Solve.
8y   -  2    =  14
​÷
8y     =
y    =
​÷
Solve.
4y   +  3    =  51
​÷
4y     =
y    =
​÷
Solve.
7y   -  9    =  54
​÷
y    =
=
​÷
Solve.
4y   +  1    =  33
​÷
y    =
=
​÷
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