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Solving Equations with Variables on both
sides
Objectives:
•To solve equations with variables on both sides of the
equal sign.
STEPS TO SOLVING LINEAR
EQUATIONS
DON’T CALL ME AFTER MIDNIGHT
•
•
•
•
•
Distribute
Combine like terms
Move the variables to one side
Add/subtract
Multiply/divide
DCMAM IS A ROAD MAP BUT NOT THE
ONLY WAY TO SOLVE AN EQUAITON
Which of the following
could be the first step?
4x + 27 = 3x
A) Subtract 4x from both sides
B) Subtract 3x from both sides
C) Subtract 27 from both sides
D) Combine like terms (4x and 3x) to get 7x
Example 1
Solve.
4x + 27 = 3x
-4x
-4x
27 = -1x
-1
-1
-27 = x
Move variable to one
side
Divide on both sides
How else can we solve
Solve.
example 1?
4x + 27 = 3x
-3x
-3x
x + 27 = 0
-27 -27
x = - 27
Move variable to one
side
Subtract on both sides
How else can we solve
Solve.
example 1?
4x + 27 = 3x
-27
4x
-3x
-27
= 3x - 27
-3x
x = - 27
Subtract on both sides
Move variable to one
side
Which of the following
could be the first step?
3(4 + 4x) = 12x + 12
A) Subtract 12x from both sides
B) Divide each term by 3
C) Distribute
D) Combine (4 and 4x) and (12x and 12)
Example 2
Solve.
3(4 + 4x) = 12x + 12
12 + 12x = 12x +12
-12x -12x
12 = 12
ALL REAL NUMBERS
•Variables cancel out
•End with same number on
both sides of =
•Means that if you plug in
any number into the equation
it will work.
distribute
notice anything?
Move variable to one side
What does this answer mean?
NO SOLUTION
•Variables cancel out
•End with different number
on both sides of =
•Means that there is no
number that will work in the
equation.
How else can we solve
example 2?
3(4 + 4x) = 12x +12
3
3
3
4 + 4x = 4x + 4
-4x - 4x
4=4
Divide each term by 3
Move variable to one side
What does this answer
mean?
ALL REAL NUMBERS
Which of the following
could be the first step?
3
(12 + 8x ) = 3( 4 + 3x )
4
A) Multiply each term by 4/3
B) Multiply each term by 4
C) Distribute
D) Combine (4 and 3x) and (12 and 8x)
Example 3
3
(12 + 8x ) = 3( 4 + 3x )
4
9 + 6x = 12 + 9x
-6x
- 6x
9 = 12 + 3x
-12 -12
-3 = 3x
3
=
3
-1 = x
distribute
Move variable to
the one side
Subtract to both
sides
Divide to both sides
How else can we solve Example 3? (Watch)
( 4) 3
(12 + 8x ) = 3( 4 + 3x ) (4)
4
Multiply all
3(12 + 8x ) = 12 ( 4 + 3x ) terms by 4
Divide 3 to both
3
3
12 + 8x = 4 ( 4 + 3x ) sides
12 + 8x = 16 +12x
-8x
- 8x
12 = 16 + 4x
-16 -16
-4 = 4x
4
4
-1 = x
Distribute
Move variable to one
side
Subtract on both
sides
Divide both sides by 4
Summary
• How would you clear the fractions in the
following problem?
2
3
5 x  x
3
4
• How do you know whether to move the
variables to the left side of the equal sign
or the right side?