# Linear Equation

**Chapter 1: Equations and Inequalities **

Linear Eqn : Statement that 2 math expressions

(called sides) are equal, with at least one

expressions containing a variable.

Admissible values of variable: values in domain.

Solutions, Roots : Any admissible variable values

that result in true expression.

Solve the Eqn: Find all solutions in solution set.

One method of solving an eqn is to replace orig

eqn by succession of equiv. eqns until soln is

obtained.

**Possible steps:**

1. Exchange sides. e.g. 3 = x → x = 3

2. Simplify, combine like terms , eliminate

parentheses. e.g. (x + 3) + 5 → x + 8

3. Add /Subtract same expression on both sides.

4. Multiply /Divide both sides by same non-zero

expression.

5. If one side zero & other side factorable , then

use zero- product property to set each factor to

zero. i.e. ab = 0 → a=0 or b=0 or both

Strategy for solving equations:

1. List any restrictions on domain of variable.

2. Successively replace eqn with equivalent eqns

using possible steps above .

3. If 2 results in product of factors = 0, use zeroproduct

property to set each to 0.

4. Check soln(s).

** Linear Equation :**

Linear Eqn in one variable: eqn equivalent to:

ax + b = 0

Also called first-degree equation.

To solve: isolate the variable

65: ( with calculator )

**Solve Applied Problems with Linear Equations
**Steps:

1. Read problem carefully, more than once. Pay

careful attention to question being asked.

Consider what a realistic solution might look

like.

2. Assign a variable for value being sought.

Express other quantities in terms of this

variable .

3. List all known facts, as math expressions.

These may be eqns involving the variable.

Draw labeled diagram, table or chart it might

help.

4. Solve eqn for variable & answer the question.

5. Chk answer with the given facts of problem.

84: Finance: A total of $10,000 is to be divided

between Sean and George, with George to

receive $3000 less than Sean. How much will

each receive?

88: Computing Hourly Wages. Leigh is paid

time-and-a-half for hours worked in excess of

40 hours and double-time for hours worked on

Sunday.

If Leigh had gross weekly wages of $342 for

working 50 hours, 4 of which were on Sunday,

what is her regular hourly rate?

90. Computer Grades. Going into the final

exam, which will count as two-thirds of the

final grade, Mike has test scores of 86, 80, 84

and 90. What score does Mike need on the final

in order to earn a B, which requires an average

score of 80?

What does he need to earn an A, which requires

an average of 90?

93. Business: Marking up the Price of Books. A

college book store marks up the price that it

pays the publisher for a book by 35%.

If the selling price of a book is $92.00, how

much did the bookstore pay for this book?

96. Business: Discount Pricing. A wool suit,

discounted by 30% for a clearance sale, has a

price tag of $399.

What was the suit’s original price?

**Assignment:**

Do problems for 1.1

Read §1.2

Do problems for 1.1

Read §1.2

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