Solving Equations With Variables on Both Sides

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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.

2

• Tools for the Tool Box!!

Distributive Property
Combining like terms
Addition Subtraction Properties of Equality
Multiplication Division Properties of
Equality
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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

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Use Steps to Solve Equation2(x 7) 3 4x - 1

• 2x 14 3 4x 1

2x 17 4x - 1
-2x -2x
17 2x - 1
1 1
4) Collect constants on same side use inverse
operations
18 2x
2 2
9 x
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Check - replace x with solution2(x 7) 3
4x - 1
2(9 7) 3 4(9) - 1
2(16) 3 4(9) - 1
2) Follow order of operations on both sides of
equation
32 3 36 - 1
35 35
X 9 is the solution to the
equation
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Use Steps to Solve Equation

• 3x 14 5x 8

-3x -3x
14 2x 8
- 8 - 8
6 2x
4) Collect constants on same side use inverse
operations
2 2
x 3
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Use Steps to Solve Equation4(1 2x) 4 6x

• 4 8x 4 - 6x

6x 6x
Get variables on same side use inverse
operation (add 6x)
4 - 2x 4
- 4 - 4
-2x 0
-2 -2
x 0
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Use Steps to Solve Equation

• 9 5x 5x 9

Get variables on same side of equation use
inverse operation (subtract 5x)
-5x -5x
9 9
The variables zeroed out and remaining is a true
statement where a number is equal to itself
this is called an identity
x any real number
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Use Steps to Solve Equation

• 6x 1 6x 8

Get variables on same side of equation use
inverse operation (subtract 6x)
-6x -6x
-1 - 8
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.
x no solutions
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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