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

left side

Every equation has 2 sides, separated

by the = sign.

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

We also use INVERSE OPERATIONS.
The inverse of multiplication is division.
The inverse of division is multiplication.
The inverse of subtraction is addition.

The inverse of addition is subtraction.

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.

+  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 inverse 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 inverse 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

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
x
4x      =  12
 4               4
+
x
-   9
9
=
=
- 9
21
3
solution
divide both sides by 4
subtract 9 from both sides
Ask yourself these questions as you solve each 
equation

1.  Can you combine like terms on the LHS?
2.  Can you combine like terms on the RHS?
3.  What side of the equation is the variable on?
4.  Is there a number being added or subtracted
to THAT side?
    (get rid of it!!  DO THE OPPOSITE
5.  Is there a number next (attached) to the variable?
    (get rid of it!!  DO THE OPPOSITE
Example 2
2p  -  3  =  27
2p         =   30
2
p      =  15
+ 3
+3
 2
add 3 to both sides
solution
divide both sides by 2
Your turn!
5y   -  15    =  20
Fill in the missing numbers.
5y     =    35
y    =
Solve these two step equations.
3y  +  8    =  23
3y     =    15
y    =
Solve these two step equations.
4y  -  1    =  15
4y     =    16
y    =
Solve these two step equations.
5y   -  4    =  36
5y     =    40
y    =
Solve these two step equations.
6y   +  7    =  37
6y     =    30
y    =
Solve these two step equations.
8y   -  2    =  14
8y     =
y    =
Solve these two step equations.
4y   +  3    =  51
4y     =
y    =
Solve these two step equations.
5y   -  1    =  29
5y     =
y    =
Solve these two step equations.
3y   +  14    =  23
3y     =
y    =
Solve these two step equations.
8y   -  11    =  21
8y     =
y    =
Solve these two step equations.
7y   -  9    =  54
y    =
=
Solve these two step equations.
4y   +  1    =  33
y    =
=
Solve these two step equations.
2y   -  13    =  1
y    =
=
Solve these two step equations.
3y   -  8    =  22
y    =
=
Solve these two step equations.
8y   -  29    =  3
y    =
=
Solve these two step equations.
9y   -  4    =  41
y    =
=
Solve these two step equations.
2y   +  7    =  17
y    =
=
Solve these two step equations.
4y   -  8    =  32
y    =
=
Solve these two step equations.
5y   +  3    =  18
y    =
=
Solve these two step equations.
7y   +  9    =  44
y    =
=
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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