Chapter 4 Simple Equations and Inequalities

1
Chapter 4 Simple Equations and Inequalities

• Section 1 Solving a Simple Equation

2
Solutions to Equations

• A number that makes an equation true is a
  solution to an equation

7
x 6 13
7 6 13
13 13
? 7 is a solution to the equation.
3
Solutions to Equations

• When you represent a situation mathematically,
  you create equations.
• My weekly paycheck, which was 795 this week,
  included overtime. Normally I my paycheck is
  625 w/out OT. How much overtime money did I
  make this week?

Regular Pay Overtime Paycheck
625 x 795
x 170
4
Solving Equations
x 2 5
x
5
Solving Equations
x 2 5
-2
6
Solving Equations
x 2 5
-2
-2
x 3
7
Solve Addition and Subtraction Equations
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Solve Addition Equations

• Solve 18 x 5

-5
-5
13 x
9
Solve Subtraction Equations

• Solve x 2.5 24

2.5
2.5
x 26.5
10
Solve Multiplication and Division Equations
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Multiplication Problems 1 of 3

• Solve -14x 112

-14
-14
x -8
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Multiplication Problems 2 of 3

• Solve -x 32

-1 x 32
-1
-1
x -32
13
Multiplication Problems 3 of 3

• Solve

14
Division Equations

• Solve

15
Solve Multi-Step Problems
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Strategy

• To solve equations, you use the idea of inverse
  operations.
• Add ? Subtract
• Multiply ? Divide
• How do you prioritize when you have more than one
  thing happening?

5x 24 16
17
Technique
1 Parentheses 2 Exponents 3 Multiplication and
Division ? 4 Addition and Subtraction ?

• Undo the additions and subtractions before you
  undo the multiplications and divisions.

5x 24 16
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Solve a Multi-Step Equation

• Solve 55 3x 40

-40
-40
15 3x
3
3
5 x
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Solve equations with more than one variable term
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Equations with more than one variable

• Solve. 6x x 21

7x 21
x 3
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Equations with more than one variable

• Solve. 2x 35 18x 13

16x 35 13
35
35
16x 48
x 3
22
Solve Equations with Variables on Both Sides
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Strategy

• 5x 15 2x 38 2x 17x

variable terms constants
24
Solve

• Solve 3x 14 - 4x

4x
4x
7x 14 0
- 14
- 14
7x -14
x -2
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Solve

• Solve 8 4x 7x 10

7x
7x
8 3x 10
- 8
- 8
3x 18
x 6
26
Handling Parentheses in an Equation
27
Using Distributive Property to Solve Equations
with Parentheses

• Solve -4(x 6) 60

-4x - 24 60
24 24
-4x 84
x -21
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Using Distributive Property to Solve Equations
with Parentheses

• Solve. 3x (7 x) 21

1
3x - 7 x 21
4x - 7 21
7 7
4x 28
x 7
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Clearing Fractions in Equations
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Clearing Fractions
6( ) ( )6

• Solve

31
Homework

• MathXL
• Ch 4 Section 1 Homework