A few more words on solving multi-step equations
Getting good at solving multi-step equations takes practice. It won’t happen overnight.
They’re an advanced topic. You might want to let them just simmer in your head for a
while. You can go plenty far on the test with just 2-step equations. Still, in case you’re
interested, here are a few additional thoughts.
An expression doesn’t have an equals sign. Here are three examples:
2x + 6
–3x + 4 – 5x + 2y + 8
3(4x – 5)
 With expressions you can simplify by combining like terms (cows with cows,
chickens with chickens, etc.) To do so, remember “Take what’s left.” Circle like
terms in different colors, together with any signs/symbols on the left of the term.
–3x + 4 – 5x + 2y + 8
simplifies to –8x + 2y + 12
 With expressions you can also simplify by using the distributive property.
3(4x – 5)
simplifies to 12x – 15
 Simplifying expressions doesn’t result in a single number at the end.
The answer is just a simpler expression.
An equation DOES have an equals sign. It sets 2 expressions equal to one another.
expression 1 = expression 2
 When you solve a one-variable equation, the answer is a statement that says
that that variable is equal to some number.
 You CANNOT combine like terms across an equals sign.
All you can do across an equals sign is the same operation on both sides.
A multi-step equation is a complicated case. Not just any detective can find the
identity of the notorious Mr. X here. If you know the TV program CSI and its offshoot
SVU, you can remember that as an acronym. (Or you can do what I did—think of a big
equation and a big SUV—but then realize that the steps outlined below actually
reverse the letters to SVU—doh!).
D. Stark 2/15/2017
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Step 1: Simplify sides separately.
-Do distributive property wherever you see it.
-Combine like terms on 1 side and then on the other
(NOT across the =).
Step 2: Get all the Variables on 1 side.
-Get them all on the left if that’s easier to remember
or get them all on the side that already has the most of them
so you can avoid negatives.
-To do this you ADD or SUBTRACT variable terms on both sides.
You are not multiplying or dividing to separate the coefficient
from the variable. You’re adding or subtracting to be able to
cross out the whole term—the variable with its coefficient.
Step 3: Do the Usual for a 2-step equation and then a 1-step one.
-For the standard 2-step equations we’re dealing with, that
means doing ADDITION/SUBTRACTION first and then
DIVISION (the opposite of PEMDAS).
EXAMPLE: 4 – 2x + 7x = 8 + 2(4x – 5)
Step 1: Before I do anything to both sides, can I simplify the left by itself? YES
4 – 2x + 7x = 8 + 2(4x – 5)
4 + 5x = 8 + 2(4x – 5)
Anything else to do on the left? NO
Still before I do anything to both sides, can I simplify the right by itself? YES
4 + 5x = 8 + 2(4x – 5)
4 + 5x = 8 + 8x – 10
Anything else to do on the right? YES
4 + 5x = 8 + 8x – 10
4 + 5x = 8x – 2
Anything else to do on the right? NO
D. Stark 2/15/2017
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Step 2: Are there variables on both sides to take care of? YES
There are more x’s on the right. If I subtract 5x from both sides I won’t have to
deal with negatives so I’m going to do that. (I could subtract 8x from both sides,
but then I’d end up with –3x on the left, which is OK but a little messy).
4 + 5x = 8x – 2
4 = 3x – 2
Step 3: Now we do the usual procedure for a standard 2-step equation.
4 = 3x – 2
6 = 3x
6 = 3x
x=2
How can I check to make sure x = 2 is the solution? I plug that value for x back into
the original equation and see if I get a true statement.
4 – 2x + 7x = 8 + 2(4x – 5)
4 – 2(2) + 7(2) = 8 + 2[ 4(2) – 5) ]
4 – 4 + 14 = 8 + 2(8 – 5)
14 = 8 + 2(3)
14 = 8 + 6
14 = 14
Yes—it checks!
D. Stark 2/15/2017
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