Transcript Introduction to Algebra

Solving Two-Step Equations
SPI 0606.3.6 Solve 2-step
linear equations
What to Write
• Whenever you see this symbol, you need to
copy the slide to your notes.
ONE STEP
EQUATIONS
Let’s Review!!!
One-Step Equations
• You only need to complete ONE STEP to
solve the equation!
Wait a
minute!
Yesterday
you said x
equals 2!
X+2
=5
X=3
ONE STEP EQUATIONS
An equation is like a balance scale
because it shows that two
quantities are equal.
What you do to one side of the
equation must also be done to the
other side to keep it balanced.
ONE STEP EQUATIONS
To solve one step equations, you need
to ask three questions about the
equation:
• What is the variable?
• What operation is performed on the variable?
• What is the inverse operation?
(The one that will undo what is being
done to the variable)
Procedure
• Isolate the variable by performing the inverse
operation on that variable.
• The inverse of subtraction is adding. The inverse
of adding is subtracting.
• The inverse of multiplication is division. The
inverse of division is multiplication.
• Perform the same operation on the side of the
equal sign that does not have a variable.
Example
y + 13 = 25
- 13 - 13
y
= 12
We want to get the y by
itself. Perform the inverse
operation. The inverse of
adding is subtracting.
Do the same operation on
the other side of the equal
sign.
Check the answer in the original
equation.
y + 13 = 25
12 + 13 = 25
25 = 25
Example 2
k – 12 = 4
+ 12 + 12
k = 16
To get k by itself, we
perform the inverse
operation. The
opposite of “minus
12” is “plus 12.”
Check
k – 12 = 4
16 – 12 = 4
4 = 4
Solving Multiplication and
Division Equations
One Step-Multiplication
Equation
Example 3 Solve 6a = 12
What is the variable?
The variable is a.
What operation is being performed on the variable? Multiplication.
What is the inverse operation (the one that will undo what is being done
to the variable)?
Division
6a = 12
6
6
a = 2
One-Step Division
Equation
Example 4 Solve b = 10
2
What is the variable?
The variable is b.
What operation is being performed on the
variable?
Division.
What is the inverse operation (the one that will undo what is
being done to the variable)?
Multiplication.
b
= 10
2
b
2 •
= 10 • 2
2
b = 20
Practice Problems
Please take a
few moments to
complete the
following
practice
problems in
your notes.
2x = 18
10x = 70
x/2 = 100
x/5 = 12
Solving 2-Step Variable
Equations
Let’s Review !!!!!
What??? I just reviewed 1-step!
Relax. You’ll use what you already know to
solve 2-step equations.
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.
STEP 2
The second step will always be either
multiplying or dividing.
Let’s try a problem
8x + 5 = 61
This
problem
has
addition,
so we
need to
subtract
first.
8x + 5 = 61
-5 -5
8x
= 56
Whatev
er we
do on
one
side,
we
have to
do on
the
other.
Now, Step 2.
This
problem
has
multiplicati
on, 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
3a - 8 = 4
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.
To Sum it all up !
2x + 4 = 14
2x + 4 = 14
-4 -4
1. Subtract 4 from both sides
2x = 10
2. Divide both sides by 2
2
2
X = 5
Now you try some problems
DO NOW!
7f + 5 = 40
12t – 6 = 90
5q – 7 = 13
4y + 8 = 32