Algebraic Expressions

Warm UpChange 0.483 to a Percent

Simplify 18x

32Simplify

%3.48

18

1

x

24

216

Like Terms

Term- a number, variable, or product of a number and one or more variables Ex.: 3a – 4b + 5 has 3 terms

Like Terms- terms with the same variables and the same exponents Ex.: 2x, 3x

4mn, 12mn In the term 3a, 3 is called the numerical coefficient

Note:

and are

NOT like terms

2xx

Simplify

bb 49

b5

17864 pp

114

17684

p

pp

Simplify

mm 38

m5

xx 135

x18

Simplify

19972 pp

127

19792

p

pp

xxx 6564

29

52464

65424

x

xxx

xxx

Solving Equations

Solving Equations

In this section we are going to learn how to solve linear (or first degree) equations.

A linear equation is one in which the exponent on the variable is 1.

Example: 5x – 1 = 3

2x + 4 = 6x - 5

Equivalent Equations

Equivalent Equations are equations that have the same solution.

The following are equivalent equations:

2x – 5 = 1

2x = 6

x = 3

When we solve an equation, we write the equation as a series of simpler equivalent equations until we obtain an equation of the form x = c, where c is some real number.

Isolate the Variable

To solve any equation, we have to isolate the variable.

That means getting the variable by itself on one side of the equals sign.

There are 4 properties we will use to isolate the variable.

Addition Property of Equality

You can add the same number to both sides of an equation and the equation remains equivalent.

Example: 159xSolve

24

240

91599

x

x

x

Subtraction Property of Equality

You can subtract the same number to both sides of an equation and the equation remains equivalent.

Example:

8

90

11191111

x

x

x

1911xSolve

Multiplication Property of Equality

You can multiply the same number on both sides of an equation and the equation remains equivalent.

Example: 36

x

Solve

18

6366

x

x

Division Property of Equality

You can divide the same number on both sides of an equation and the equation remains equivalent.

Example: 284 xSolve

74

28

4

4

x

x

Procedure to Solve Equations

1. Get rid of fractions.

2. Distribute when needed.

3. Combine like terms on same side of equals.

4. Use the addition/subtraction property. You may have to use it more than once!

5. Solve using either the multiplication property or the division property.

Solve

8224 x

204

80

4

4

804

282224

x

x

x

x

6552 x

302

60

2

2

602

565552

x

x

x

x

Solve

3875 a

95

45

5

5

455

738775

a

a

a

a

12318 y

23

6

3

3

63

181231818

y

y

y

y

Solve

a

a

a

a

a

aa

1711

17

17

1313134

134

87134

aa 87134 11743 aa

41

4

1

4

71177

117

a

a

a

a

a

Variables on Both Sides

Your goal is to get the variable on one side of the equals sign and everything else on the other side of the equals sign.

Always combine like terms on each side of the equation FIRST!

Example: 854 xx

3

133

13

3

3

133

58553

853

854

x

x

x

x

x

xxxx

Solve

1234 xx

33

9

3

3

93

312333

1233

1234

x

x

x

x

x

xxxx

423 xx

4

42223

x

xxxx

Solve

8342 xxx

14

4

4

4

44

48444

844

845

845

x

x

x

x

x

xxxx

xx

xx 9107

x

x

x

x

x

10

1710

10

10

17

1017

101010107

10107

Grouping Symbols

You have to distribute before you combine like terms.

Solve

732 xx

1

6766

76

762

762

x

x

x

xxxx

xx

18322 x

34

12

4

4

124

618664

1864

x

x

x

x

x

Solve

11435 x

x

x

x

x

x

x

23

3

3

6

36

11315

135

111235

xxx 712320

92

18

2

2

182

20222020

2220

2555320

25320

722320

x

x

x

x

x

xxxx

xx

xxx