Warm-Up: September 29, 2015 Solve for x

62

1

5)4

52329124)3

13253)2

7285)1

xx

xx

xx

x

Ohms

Page 67 #70 Answer

Homework Questions?

Linear EquationsSection P.7

An expression is an algebraic statement that does not have an “=“

An equation is two expressions joined by an “=“

Expression vs. Equation

A linear equation (in x) is one that can be written in the form

Linear Equation

0,,

0

aba

bax

ℝ

The following all mean basically the same:◦Solve for x◦Find the solutions◦Find the roots◦Find the zeros

Solving a Linear Equation

Multiply both sides by the least common denominator (LCD)

Then solve as before

Linear Equations with Fractions

Warm-Up #4

62

1

5

xx

Has the variable in a denominator Must check for domain restrictions Then solve as before

◦ Multiply by LCD to clear denominators

Equations with Rational Expressions

Example 4

xx 3

1

18

1

9

8

2

5

You-Try #4

x

x

x 5

47

5

94

Example 5

25

32

5

2

5

42

xxx

You-Try #5

4

12

2

3

2

52

xxx

A conditional equation has a limited number of real solutions, but at least one◦ If you can solve and get x = #, and # is not a

domain restriction An inconsistent equation has no real

solutions◦ All x’s are eliminated and left with a false

statement such as “7=0” An identity has an infinite number of

solutions, often all real numbers◦ All x’s are eliminated and left with a true

statement such as “3=3”

Types of Equations

Solve S = P + Prt for t

You-Try #7: Solving a Formula

The absolute value of a number is its distance from zero.

|x| = a means x = a or x = -a Solving an absolute value equation:1. Isolate the absolute value.2. If the absolute value equals a negative,

there are no solutions. Otherwise, split the equation into two equations: one equal to positive, one equal to negative.

3. Solve each equation for x.

Absolute Value

Example 9

174123 x

You-Try #9

2212242 x

Read Section P.7 Page 81 #1-101 Every Other Odd, 108

Show work, or you will not receive credit

Assignment

In Exercises 1-16, solve and check each linear equation.

Exercises 17-30 contain equations with constants in denominators. Solve each equation.

7

25

3

1)29

4

5

8

3

6

3)25

13

2

5

3)21

223

)17

71316)13

52723)9

672)5

7257)1

xx

xx

xx

xx

xx

xx

xx

x

In exercises 51-58, determine whether each equation is an identity, a conditional equation, or an inconsistent equation.

In Exercises 59-70, solve each equation or state that it is true for all real numbers or no real numbers.

In Exercises 71-90, solve each formula for the specified variable.

43

6

3

2)57

3232)53

xx

x

xx

9

364

3

12

3

4)69

4

3

2

12)65

23

2

2)61

2

2

x

x

xx

x

x

x

x

x

abahA

mmcE

bbhA

for )81

for 77)

for )73

21

2

21

In exercises 51-58, determine whether each equation is an identity, a conditional equation, or an inconsistent equation.

In Exercises 59-70, solve each equation or state that it is true for all real numbers or no real numbers.

In Exercises 71-90, solve each formula for the specified variable.

43

6

3

2)57

3232)53

xx

x

xx

9

364

3

12

3

4)69

4

3

2

12)65

23

2

2)61

2

2

x

x

xx

x

x

x

x

x

ffqp

SVS

FB

abahA

mmcE

bbhA

for 111

)89

for )85

for )81

for 77)

for )73

21

2

21