Solving Two-Step Linear Equations by tiw14488

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									Solving Two-Step Linear
       Equations
       Pre-Algebra
       Mrs. Murphy
    Indiana Academic
    Standard
   Mathematics, 7th Grade
        Standard 3: Algebra and Functions
             Students express quantitative relationships
              using algebraic terminology, expressions,
              equations, inequalities, and graphs.
        7.3.2 : Write and solve two-step linear
         equations and inequalities in one variable
         and check the answer.

     Link
Order of Operations
 PRIMARILY          ISOLATE VARIABLE

 • Multiplication   • Addition
 • Division         • Subtraction

  before            then

 • Addition         • Multiplication
 • Subtraction      • Division
Remember
     Isolate   Variable


     Always    CHECK
     your answer by
     substitution
Review      (One-Step Equations)

Solve: 3y = 15

Step 1
  3y/3 = 15/3
     y=5

   Check: 3y = 15
    3(5) = 15
      15 = 15
Review       (One-Step Equations)

Solve: 4r = -56

Step 1
  4r/4 = -56/4
     r = -14

   Check: 4r = -56
    4(-14) = -56
       -56 = -56
Algebra Steps

            2x + 7 = 11

         + -7 to both sides

       divide both sides by 2

               x=2
Solving Two-Step
Equations
 Solve: 2x + 5 = 29
                          CHECK:
 Step 1
   2x + 5 – 5 = 29 – 5         2x + 5 = 29
                            2(12) + 5 = 29
           2x = 29 – 5         24 + 5 = 29
           2x = 24                 29 = 29


 Step 2
   2x/2 = 24/2
      x = 12
Solving Two-Step
Equations
 Solve: 2x – 5 = 71

                          CHECK:
 Step 1
   2x – 5 + 5 = 71 + 5       2x – 5 = 71
           2x = 71 +5        2(38) – 5 = 71
           2x = 76              76 – 5 = 71
 Step 2                             71 = 71
   2x/2 = 76/2
      x = 38
Practice Problems

   3x – 5 = 16

   -6z + 15 = 3

   8a – 7 = 65

   7x + 3 = -4
Recall


 • When solving an inequality

   – Switch direction of inequality sign when
     multiplying or dividing by a negative
     number
Solving Two-Step Inequalities
Solve: -5x – 2 > 18
                          Graphically the solution is:
Step 1
   -5x – 2 + 2 > 18 +2
           -5x > 18 + 2
                                                    -4
           -5x > 20
(flip inequality sign)
Step 2
   -5x/-5 < 20/-5
        x < -4
Practice Problems

  x+3<2

  9z – 6 > 3

  -2y – 4 > 14

  -7a + 14 < 28
       Homework / Group Work
   2 Worksheets - Even Problems ONLY

   Tomorrow - Computer Lab
      Additional Information




 Two-Step Equations & Inequalities

 Solving Inequalities: An Overview

								
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