It’s a party!
Solving Multi-step Equations
A GEMS Submission for ALEX
Submitted by: E. Thompson, PhD.
Summer 08
Review of One-Step Equations
2x = 8
x
 18
3
x +3 = 15
x – 5 = 20
Be sure you can solve each type of problem before we begin!
With Multi-Step Equations it can
be hard to know where to start….
pretend it’s a party!
You are the host - a.k.a. ‘X’
In what order do people leave a party?
–
Enemies (get rid of them to avoid trouble)
– Acquaintances (after mingling with everyone, they
usually leave early)
–
Friends (they hang out with the host a little longer)
– Family (if attending, they will stay to the end to help clean)
Who is who?
Consider our one-step equations
2x = 8
x
 18
3
x +3 = 15
x – 5 = 20
FAMILY….right beside
you…and only you… until the
end!
FRIENDS….they are close to
you…they stay longer than
some people, but not as long
as family
Who are the acquaintances?
2x  5
7
3
ACQUAINTANCE –
Because this number mingles with all other
many parts of the equation instead of giving
most of its attention to the host (x), it is not a
friend…it is an acquaintance.
Identify all the Party-goers
FRIEND
FAMILY
2x  5
7
3
ACQUAINTANCE
The equal sign is the door…who
goes out the door first?
2x  5
7
3
ACQUAINTANCE –
multiply each side of
the equation by 3.
The work:
 2x  5 
3
  37 
 3 
The result:
2 x  5  21
We still have company... lets continue….
Who is next to leave?
2 x  5  21
Friends – add
5 to each side.
The work:
2 x  5  5  21  5
The result:
2 x  26
All that is left is family…a familiar one-step equation.
Clean up the party with
a family member
2 x  26
The work:
2 x 26

2
2
The result:
x  13
Family –
divide each
side by 2
Don’t forget to check your work with Order of Operations!
Try these problems:
2 x  13  55
Steps:
x2
6
3
1. Identify the party-goers
2. Eliminate party-goers in order
3. Get x (the host) alone
4. Check your solution
x
47
3
Enemies can ruin the entire
party…get rid of them first!
1  2x  6 

4
3 3 
Its easy to spot
an enemy…they
affect
everything!
To solve, multiply each side by the reciprocal
The work:
3 1  2x  6 
3
 
  4
1 3 3 
1
The result: 2 x  6
 12
3
Try to complete the
problem from
here….the answer is:
21
Its party time!
Do you know who is in your home?
Family
HOST
Enemy
Friend
5  3x  9 

  10
3 3 
The
Door!
Acquaintanc
e
See if you can ID the enemy, the friend, the acquaintance, a
family member, the host and the door!
The more you party, the more
responsible you will become!

TIPS:
–
–
–
Enemies and acquaintances are very similar…both
affect the entire equation. Typically there are only
enemies when you have already identified an
acquaintance.
Eventually, you will partiers outside the door
(operations on both sides of the equal sign). Start these
by using the same method to get everyone on one side..
If you find yourself (the host) in two places at once
(variables on both sides of the equal sign), use the same
method to regroup yourself back into the house.