Solving two-step equations Chapter 4.1

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Solving two-step equationsChapter 4.1

• Arizona State Standard S3C3PO3 Analyze
  situations, simplify, and solve problems
  involving linear equations and inequalities using
  the properties of the real number system.

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Objective

• I will use two operations to solve a two step
  equation.
• I will solve real-life problems using two step
  equations.

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Ultimate Goal

• ISOLATE THE VARIABLE
• Ask yourself???
• How is the variable attached?

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Addition property of equality

• 2 x 5 9
• 2x 5 -5 9 -5
• 2x 4
• 2x 4
• 2 2
• x 2

Subtract 5 from both sides
Simplify
Divide both sides by 2
Simplify
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Check

• To see that 2 is the solution, replace x in the
  original equation with 2.
• 2 x 5 9
• 2 (2) 5 9
• 4 5 9
• 9 9

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Give it a try

• 3 x 6 12
• 3x 6 6 12 6
• 3x 6
• 3x 6
• 3 3
• x 2

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Give it a try!

• 4.5 3 2.5 x
• 4.5 3 3 2.5 x 3
• 1.5 2.5 x
• 1.5 2.5 x
• 2.5 2.5
• 0.6 x

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Check

• 0.6 2 3.5c
• 0.6 2 3.5 (0.4)
• 0.6 2 1.4
• 0.6 0.6

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Real-Life Situation

• You are joining a community tennis club. The
  annual membership fee is 50, and a tennis court
  rents for 10 per hour. You plan to spend no
  more than 190 playing tennis during the year.
  How many hours can you play?
• Step 1
• Translate
• Total spent annual fee hourly rate x hours of
  tennis

10

• You are joining a community tennis club. The
  annual membership fee is 50, and a tennis court
  rents for 10 per hour. You plan to spend no
  more than 190 playing tennis during the year.
  How many hours can you play?
• Total spent annual fee hourly rate x hours of
  tennis
• Step 2
• Label the constants, identify the variable
• Total spent 190
• Annual Fee 50
• Hourly Rate 10
• Number of hours played n

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• You are joining a community tennis club. The
  annual membership fee is 50, and a tennis court
  rents for 10 per hour. You plan to spend no
  more than 190 playing tennis during the year.
  How many hours can you play?
• Total spent annual fee hourly rate x hours of
  tennis
• Step 3
• Substitute the constants into the algebraic
  equation.
• 190 50 10 x n

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Step 4 Isolate the variable

• 190 50 10 x n
• 190 50 50 50 10 x n
• 140 10 x n
• 10 10
• 14 n

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Does it make sense?

• The question asked.How many hours can you play
  for 190? There is a 50 membership fee and each
  hour on the court cost 10.
• Does the answer of 14 hours make sense???

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Practice

• Page 160
• 1 3
• 9 - 24

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Chapter 4.2

• Solving Multi-Step Equations

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Objective

• I will combine like terms and use the
  distributive property to solve equations.

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Ultimate Goal

• ISOLATE THE VARIABLE
• Ask yourself???
• How is the variable attached?

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Combing Like Terms

• Before using inverse operations to solve an
  equation, you should check to see whether one or
  both sides of the equation can be simplified by
  combining like terms.
• Like Terms Two or more terms in an expression
  that have the same variables raised to the same
  powers.

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Solve Combining Like Terms

• -13 3 n 3 n
• -13 3n 3 n
• -13 4 n 3
• -16 4 n
• -4 n

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Solve Combining like terms

• -6 x 1 5x 3
• -6x 1 5x 3
• -x 1 3
• -x 1 1 3 1
• -x 4
• -1 -1
• x -4

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Give it a try!

• -2x 2 4x 20
• -2x 2 4x 20
• -6x 2 20
• -6x 2 2 20 2
• -6x 18
• -6 -6
• x -3

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Distributive Property

• 2 (x 3) 10
• 2(x 3) 10
• 2x 6 10
• 2x 6 6 10 6
• 2x 16
• 2 2
• x 8

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Give it a try!

• 4 (x 2) 10
• 4x 8 10
• 4x 18
• x 18 4
• x 4 ½

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Distributing a Negative

• 2 (3x - 4) 2

It can help to rewrite as -1
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Practice Time ?

• Page 164 1 6, 19
• 3x x 8 -16
• Step 1 Combine like terms
  3x x 2x
• 2x 8 16
• Step 2 Inverse Operation (subtract 8) 2x
  8 8 -16 - 8
• Whatever you do to one side, you MUST do to the
  other.
• Remember to Keep, Change, Change
• 2x -24
• Step 3 Inverse Operation (Divide by 2) 2x
  2 -24 2
• Remember Different Sign
  NEGATIVE x -12
• HOMEWORK 7 - 21

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Practice Time ?

• Page 164 1 6, 19
• 19. 5 3 (x 1) 5
• Step 1 Use the Distributive Property to get rid
  of the parenthesis -3(x1) -3x - 3
• Step 2 Rewrite the problem
  5 -3x 3 5
• Step 3 Combine like terms
  5 -3 2
• Step 4 Rewrite the problem
  2 3x 5 OR -3X 2 5
• Step 5 Inverse Operation (subtract 2)
• Whatever you do to one side, you MUST do to the
  other.
• Remember to Keep, Change, Change