Solving Two-Step Equations

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Solving Two-StepEquations

• You will solve equations by undoing operations
  using properties of equality.
• Essential Question How do you solve two-step
  equations?
• TP Construct and solve two step equations for
  real world problems by combining like terms

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Whatever you do to one side, you must do to the
other side to keep property of equality.

• Steps for Solving Two-Step Equations
• Solve for any Addition or Subtraction on the
  variable side of equation by undoing the
  operation from both sides of the equation.
• Solve any Multiplication or Division from
  variable side of equation by undoing the
  operation from both sides of the equation.
• Inverse Operations
• Addition ? Subtraction
• Multiplication ?Division

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• Example 1 Solve 4x 5 15
• 4x 5 15
• 5 5 (Add 5 to both sides)
• 4x 20 (Simplify)
• 4 4 (Divide both sides by 4)
• x 5 (Simplify)
• Check
• 4(5) -5 15
• 20 5 15
• 15 15

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EXAMPLE 2
Solve a two-step equation
Write original equation.
Subtraction Property of Equality
Simplify.
Multiplication Property of Equality.
Simplify.
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EXAMPLE 2
Solve a two-step equation
CHECK
Write original equation.
Substitute 12 for x.
Simplify. Solution checks.
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for Example 1 2
GUIDED PRACTICE
Solve the equation. Check your solution.
1. 5x 9 24
SOLUTION
Write original equation.
Subtraction Property of Equality
Simplify.
Division Property of Equality
Simplify.
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for Example 1
GUIDED PRACTICE
CHECK
Write original equation.
Substitute 3 for x.
Simplify. Solution check.
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for Example 1
GUIDED PRACTICE
Solve the equation. Check your solution.
2. 4y 4 16
SOLUTION
Write original equation.
Addition Property of Equality
Simplify.
Division Property of Equality.
Simplify.
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for Example 1
GUIDED PRACTICE
CHECK
Write original equation.
Substitute 5 for y.
Simplify. Solution checks.
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for Example 1
GUIDED PRACTICE
Solve the equation. Check your solution.
SOLUTION
Write original equation.
Add 7 to each side.
Simplify.
Multiply each side by 3.
Simplify.
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for Example 1
GUIDED PRACTICE
CHECK
Write original equation.
Substitute 18 for z.
Simplify. Solution checks.
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EXAMPLE 3
Solve a two-step equation by combining like terms
Solve 7x 4x 21
7x 4x 21
Write original equation.
3x 21
Combine like terms.
Divide each side by 3.
x 7
Simplify.
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for Examples 3
GUIDED PRACTICE
Solve the equation. Check your solution.
5. 8t 3t 35
8t 3t 35
Write original equation.
5t 35
Substract the like terms
Divide each side by 5
t 7
Simplify.
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for Examples 3
GUIDED PRACTICE
Write original equation.
Substitute 7 for t.
Multiply.
35 35
Simplify. Solution checks.
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for Example 4
GUIDED PRACTICE
Jobs
10. Kim has a job where she makes 8 per hour
plus tips. Yesterday, Kim made 53
dollars, 13 of which was from tips. How many
hours did she work?
SOLUTION
53 13 8h
Write the equation
5313 13 13 8h
Subtraction Property of Equality.
40 8h
Simplify.
5 h
Division Property of Equality
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for Example 4
GUIDED PRACTICE
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Essential Question

• How do you solve two-step equations?