Transcript Solving 2-Step Variable Equations

Solving 2-Step Variable
Equations
Two Step Equations Essential
Question
How are inverse operations used to
solve two step equations?
Why does order matter when solving
two step equations?
What??? I just learned 1-step!
Relax. You’ll use what you already know
to solve 2-step equations.
Solving Two-Step Equations
To find the solution to an equation we must
isolate the variable. In other words, get the
variable on one side of the equation by
itself.
We isolate the variable by performing
operations that will eliminate (cancel) the
other numbers from the expression.
Solving Two-Step Equations
We have seen how to eliminate a constant
(Addition Property of Equality) & how to
eliminate a coefficient (Multiplication
Property of Equality).
What if an equation has both a constant
and a coefficient to be eliminated?
This is called a Two-Step Equation.
So, what’s first?
You need to break up the equation into its
two steps.
STEP 1
The first step will always be either adding or
subtracting. (Think: Order of Operations
backwards)
STEP 2
The second step will always be either
multiplying or dividing.
Let’s try a problem.
This
problem has
addition, so
we need to
subtract
first.
8x + 5 = 61
-5 -5
8x
= 56
Whatever
we do on
one side,
we have to
do on the
other.
Now, Step 2.
This problem
has
multiplication,
so we need to
divide now.
8x = 56
8
8
x = 7
Whatever we
do on one
side, we have
to do on the
other.
Let’s try another problem.
This
problem has
subtraction,
so we need
to add first.
3a - 8 = 4
+8 +8
3a
= 12
Whatever
we do on
one side,
we have to
do on the
other.
Now, Step 2.
This problem
has
multiplication,
so we need to
divide now.
3a = 12
3
3
a = 4
Whatever we
do on one
side, we have
to do on the
other.
Let’s try another problem.
This
problem has
addition, so
we need to
subtract
first.
z + 2 = 26
6
-2 -2
z
6
= 24
Whatever
we do on
one side,
we have to
do on the
other.
Now, Step 2.
6 • z = 24 • 6
6
This problem
has division,
so we need to
multiply now.
z = 144
Whatever we
do on one
side, we have
to do on the
other.
Let’s try one more problem.
This
problem has
subtraction,
so we need
to add first.
m - 10 = 15
5
+10 +10
m
5
= 25
Whatever
we do on
one side,
we have to
do on the
other.
Now, Step 2.
5 • m = 25 • 5
5
This problem
has division,
so we need to
multiply now.
m = 125
Whatever we
do on one
side, we have
to do on the
other.
Trick Question
Does order matter when solving two step
equations? Why or Why not?
Order does matter because if you do any
other math operation other than addition or
subtraction first, you will end up with an
incorrect solution