CECS 5260

Computer Graphic for

Mediated Communications

I. Sheffield Assignment 4 August 6, 2012

Solving Equations

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Solving Equations

Title Page Navigation Table of Contents Terminology Solving Equations Solving Equations with Fractions Solving Radical Equations Summary

Table of Contents

Solving Equations

Terminology

Coefficient – The number part in a multiplication expression. For example 4 is the coefficient in the expression 4s.

Constant – is a number that is added or subtracted in an expression. For example, 5 is the constant in the expression c+5.

Distributive Property – Multiplication a distributes over addition. For example 3(x+2) = 3*x + 3 * 2 = 3x + 6

Equation – Has an equal sign, and shows a relationship.

Exponents – Tells how many times a number is multiplied times itself.

Like Terms – terms with exactly the same variable parts (the same letters and exponents). The coefficients may be different.

Solving Equations

Solving Equations

Terminology

Least Common Denominator (LCD) – The smallest number that is a multiple of a group of denominators.

Radicals – a radical sign with a radicand

Power Rules - If both sides of an equation are raised to the same power all solutions of the original equation are also solutions of the new equation.

Addition Property of Equality

If

then cbca

ba

Examples:

5

71277

127

x

x

x

13

31033

103

a

a

a

Solving Equations

Multiplication Property of Equality

If

then bcac

ba

Examples:

44

12

3

3

123

x

x

x

122

24

2

38

3

2

2

3

83

2

x

x

x

x

Solving Equations

Steps for Solving an Equation• Distribute

• Combine Like Terms

• Addition Property of Equality

• Multiplication Property of Equality

• Check your solution

Solving Equations

Example of Combining Properties:

y

y

y

y

y

y

92

2

2

18

218

882810

8210

)4(210 Distribute

Addition Property of Equality

Multiplication Property of Equality

Solving Equations

Example of Combining Properties:

h

h

h

h

h

hhhh

hh

hh

hh

37

7

7

21

721

15157156

1576

15512556

151256

11612953

1)43(4953

Distribute

Combine Like Terms

Addition Property of Equality

Addition Property of Equality

Multiplication Property of Equality

Solving Equations

Solving Equations

Steps for Solving an Equation with Fractions

• Distribute

• Find LCD (Least Common Denominator)

• Multiply the whole equation by the LCD (Clearing the Fraction)

• Combine Like Terms

• Addition Property of Equality

• Multiplication Property of Equality

• Check your solution

Example of Clearing Fractions1 3 1

(7 2)8 4 167 1 3 1

8 4 4 1616

7 1 3 116

8 4 4 16

14 4 12 1 16

26 4 1 16

26 16 4 1 16 16

10 4 1

10 4 4 1 4

10 5

1

2

x x x

x x x

LCD

x x x

x x x

x x

x x x x

x

x

x

x

Solving Equations

Solving Equations

Steps for solving radical equations:  Isolate the radical on one side of the equation. (If your equation has two or more radicals isolate one of the radicals by itself on one side of the equal sign and the other radical on the other side) Apply the power rule – Raise both sides of the equation to a power that is the same as the index of the radical Solve the equation – If it still contains a radical repeat steps 1 & 2. Check your answer– It is essential that all potential solutions be tested in the original equation.

Solving Equations

20

20

603

6443

8)43(

84322

x

x

x

x

x

Example of Solving Radical Equations

Solving Equations

11

2

01

02

0)1)(2(

0239

018279

2530973

5373

3573

5373

2

2

2

22

x

x

x

x

xx

xx

xx

xxx

xx

xx

xx

Example of Solving Radical Equations

Summary:Always follow the Steps for Solving Equations

Remember you can only combine like terms (terms that have the same variable and exponent)

Always move your variable term before your constant

Finally, check your answer.

Solving Equations