# Solving Two-Step Linear Equations by xab70192

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Solving Two-Step Linear
Equations
Pre-Algebra
Mrs. Murphy
Standard
   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

Order of Operations
PRIMARILY          ISOLATE VARIABLE

• Division         • Subtraction

 before            then

• Subtraction      • Division
Remember
 Isolate   Variable

 Always    CHECK
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