Solving 2 step Equations

It is important to learn this process, so that

you can apply it to more difficult equations!

Solving Two-Step Equations

To solve an equation, we must isolate

the variable (get the variable on one side

all by itself.)

Every equation has 2 sides, separated

by the = sign.

left side

4 + x

=
12
right side

The solution to an equation is expressed

as an equation with the variable ALONE

on one side.

The solution is :   y = 2

example:    y + 3 = 5

To islolate the variable, we use what we know about

 the IDENTITY properties.

We know that x - 0 = x
We know that 
We know that 1x = x.
We know that x + 0 = x
 x
1
=
x

  •  Each side of an equation can be multiplied

by the same non-zero number without

changing the solution.

•  Each side of an equation can be divided by

the same non-zero number without

changing the solution.

• The same number can be subtracted from

both sides of the equation without changing

the solution.

• The same number can be added to both sides

of the equation without changing the solution.

We also use the PROPERTIES of EQUALITY

Think of these properties as the Golden Rule:

       3 = 3

3 + 2 = 3 + 2

What you do to one side of the equation,

you MUST do to the other.

    4 = 4

4(6) = 4(6)

      7 = 7

7 - 5 = 7 - 5

     16 = 16

 16÷8 = 16÷8

We also use INVERSE OPERATIONS.

The inverse of addition is subtraction.

The inverse of subtraction is addition.
The inverse of multiplication is division.
The inverse of division is multiplication.
Example  1

The inverse 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.

Inverse and Equality
We want to isolate the variable p.
Identity
+  9  =  12
p  +  0  =  3
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.

We want to isolate the variable s.
Inverse and Equality

The inverse of subtraction is addition, so we need

to add 3 to both sides of the equation.

Identity

s

s   -  0   =    20
 -  3  =  17

+

3

=
+ 3

20

You must show

the steps of

solving your

equations!

Example  3

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

We want to isolate the variable x.
Inverse and Equality

The inverse of multiplication is division, so we need

to divide both sides of the equation by 5.

Identity

÷

  1x     =      7
 5x    =     35

5

x

=

÷  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

inverse operations to

 

undo ADDITION or

SUBTRACTION BEFORE

undoing MULTIPLICATION or DIVISION.

 

 

 

Use inverse operations to undo the constant

before undoing the coefficient.

Coefficient
4
x
+
9
=
21
Constant
Example 1
4
4x   +  0    =   12
x
 4                4
+
4x      =  12
-   9
1x
9
x
=
=
=
- 9
21
3
3
subtract 9 from both sides
divide both sides by 4
solution
Example 2
2p  -  3  =  27
2p  -  0      =  30
2
2p         =   30
1        =  15
+ 3
p      =  15
+3
 2
add 3 to both sides
divide both sides by 2
solution
Your turn!
5y  -  15  =  20
5y    -  0    = 
+
Fill in the missing numbers.
5y     =    35

 

1y
y    =
=
+
35
Fill in the missing operations and numbers.
9c  +  3   =  39
9c  +  0    =  
9c      =
1c
3
c   =
=
3
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

Remember:

FIRST, undo any addition or subtraction.

What you do to one side of the equation, you must

do to the other.  SHOW your work on both sides!

THEN, undo any multiplication.
Use inverse operations to isolate the variable.
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