Chapter 3.4 Notes: Solve Equations with Variables on Both Sides

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Chapter 3.4 Notes Solve Equations with Variables
on Both Sides

• Goal You will solve equations with variables on
  both sides.

2

• Some equations have variables on both sides.
• To solve such equations, you can collect the
  variable terms on one side of the equation and
  the constant terms on the other side of the
  equation.

3

• Steps for Solving Linear Equations
• Step 1 Use the distributive property to remove
  any
• grouping symbols.
• Step 2 Simplify the expression on each side of
  the
• equation.
• Step 3 Use properties of equality to collect
  the
• variable terms on one side of the
  equation
• and the constant terms on the other
  side of
• the equation.
• Step 4 Use properties of equality to solve for
  the
• variable.

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• Step 5 Check your solution in the original
  equation.
• Ex.1 Solve 7 8x 4x 17
• Ex.2 Solve 13 5x 2x 8
• Solve the equation. Check your solution.
• Ex.3 9 3k 17 2k
• Ex.4 3 4a 5(a 3)

5

• Ex.5 The equation
  is solved below.
• Step 1 6x 5 4x 15
• Step 2 10x 5 15
• Step 3 10x 20
• Step 4 x 2
• Which is the first incorrect step in the
  solution?
• A. Step 1 B. Step 2 C. Step 3
  D. Step 4

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• Ex.6 The equation
  is solved below.
• Step 1 4x 5 x 19
• Step 2 3x 5 19
• Step 3 3x 24
• Step 4 x 8
• Which is the first incorrect step?
• A. Step 1 B. Step 2 C. Step 3
  D. Step 4

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• Ex.7 Solve
• Ex.8 2(x 4) 2x 8(x 3)
• Ex.9 9(x 3) 3x 3(x 4) 6
• Ex.10 2(x 4) -6(x 7)
  .

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• Number of Solutions
• Equations do not always have one solution.
• An equation that is true for all values of the
  variable is an identity.
• An identity has all real numbers as solutions.
• Some equations have no solution.

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• Solve the equation.
• Ex.8 3x 3(x 4) Ex.9 2x 10
  2(x 5)
• Solve the equation, if possible.
• Ex.10 3(2a 2) 2(3a 3)
• Ex.11 9z 12 9(z 3)
• Ex.12 7w 1 8w 1
• Ex. 13 5x 6 5(x 1)

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• Ex.14 4(3x 2) 2(6x 4)

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Example 15
Solve a real-world problem
CAR SALES
The annual sales report for a car dealership is
shown. If these trends continue, in how many
years will the number of new cars sold be twice
the number of used cars sold?
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Example 15
Solve a real-world problem
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Example 15
Solve a real-world problem
(
)
Write equation.
78

6x

2
4x

67
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Example 15
Solve a real-world problem
CHECK You can use a table to check the solution.
0
4
3
Year
1
2
67
63
59
55
51
Used cars sold
78
84
90
96
102
New cars sold