Download Solve Equations With Variables on Both Sides

Solving Equations With
Variables on Both Sides
Lesson Objective:
To use what we already know about to
solve multiple step equations with
variables on both sides.
Tools for the Tool
Box!!
Steps to Solve Equations
with Variables on Both Sides





Eliminate ( ) on both sides of equation
using the distributive property.
Combine any like terms on both sides.
Collect variable on one side of the equation
Collect constants on the other side of the
equation
Solve
Use Steps to Solve Equation:
2(x + 7) + 3 = 4x - 1
2x + 14 + 3 = 4x – 1
2x + 17 = 4x - 1
-2x
-2x
17 = 2x - 1
+1
+1
18 = 2x
2
2
9= x
1) Eliminate ( ) --distribute
2) Combine like terms
3) Collect variables on same
side – use inverse operation
4) Collect constants on
same side – use inverse
operations
Check - replace “x” with solution
2(x + 7) + 3 = 4x - 1
2(9 + 7) + 3 = 4(9) - 1
2(16) + 3 = 4(9) - 1
32 + 3 = 36 - 1
35 = 35
X=9
1) Replace X = 9
2) Follow order of
operations on both
sides of equation
3) Checks
is the solution
to the equation
Use Steps to Solve Equation:
3x + 14 = 5x + 8
-3x
-3x
14 = 2x + 8
-8
-8
6 = 2x
2 2
x= 3
2) Combine like terms
3) Collect variables on same
side – use inverse operation
4) Collect constants on
same side – use inverse
operations
Use Steps to Solve Equation:
4(1 – 2x) = 4 – 6x
4 – 8x = 4 - 6x
+6x
+ 6x
4 - 2x = 4
-4
-4
-2x = 0
-2 -2
x= 0
Get rid of ( ) -- distribute
Get variables on same side
– use inverse operation
(add 6x)
Solve 2 step equation
Use Steps to Solve Equation:
9 + 5x = 5x + 9
-5x -5x
9=9
x = any real
number
Get variables on same side
of equation – use inverse
operation (subtract 5x)
The variables zeroed out
and remaining is a true
statement where a
number is equal to itself –
this is called an identity
The solution is all real
numbers
Use Steps to Solve Equation:
6x – 1 = 6x – 8
-6x
-6x
Get variables on same side
of equation – use inverse
operation (subtract 6x)
-1 = - 8
x = no solutions
The solution is no real
numbers or empty set
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The variables zeroed out
and remaining is a false
statement where a
number is equal to a
different number, so there
will be no number that will
work in the equation.
Review Steps to Solve Equations
with Variables on Both Sides
 1)
Get rid of ( ) on both sides of
equation.
 2) Combine like terms on both sides.
 3) Get variable on one side of the
equation.
 4) Solve 2 step equation by undoing
what has been done to the variable.
 5) Remember 2 special cases when the
variable zeros out.
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The end
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