Download Solve Equations With Variables on Both Sides

Solve Equations With Variables on
Both Sides
Section 2.5 Beginning on page 104
1
Variables on Both Sides
In the previous lesson we laid out the steps to solving multi-step equations.
We will expand on that a bit and add one additional step to account for this
new situation.
*Remember, being consistent in your steps will
lead to basic algebra becoming routine for you.
First : Simplify each side separately
Distribute
Combine like terms
Second : If there are variables on both
sides, eliminate one.
Third: Get the variable term alone
Fourth: Get the variable alone
2
Avoiding a Common Mistake
This is why I say that if the equation is simplifies and there are variables on
both sides, you should eliminate one of the variables before working with the
constants.
Students tend to
move the equal sign
when there is
nothing on one side.
When there are no
terms left on one
side, that side is
equal to 0.
3
It is perfectly acceptable to
subtract 5 from both sides or
add ten to both sides.
Now lets say you decide to
subtract the 5x to eliminate
the extra variable term.
This can be mostly avoided by always
dealing with the variable terms first.
Example
Solve:
You could eliminate the fraction here by
multiplying by the denominator, but since 16
and 60 are both divisible by 4 the fraction will
be eliminated when we distribute.
Always work to eliminate the “stuff”
on the same side as the variable at
this point.You wouldn’t want to
subtract 15 from both sides.
Side Note: Multiplying by a unit fraction is the same as
dividing by the denominator of the unit fraction.
Unit Fractions :
4
Practice
Solve each equation. Check your solutions.
Think ahead : Why wouldn’t you want to
subtract 5m from both sides?
1)
2)
3)
4)
5)
6)
Did you check your solutions?
5
Number of Solutions
The majority of linear equations you solve will have exactly one solution. There
are also two other possibilities. The equation may have no solutions, and the
equation may have infinitely many solutions.
1)
When you end up with a statement that can
not be true, that indicates that no possible
value of the variable is a solution.
Nonsense!
No Solution
6
Number of Solutions
2)
When you end up with a statement that is
always true, that indicates that every
possible value of the variable is a solution.
Of Course!
All Real Numbers
or
Infinitely Many Solutions
***When an equation is true for all values
of the variable that equation is an identity.
7
As soon as you can see that
both sides are identical, you
know that the equation is an
identity and you can stop.
Practice
Solve the equation, if possible.
7)
8)
No Solution
8
9)
All Real Numbers