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
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
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
1. Read problem carefully, more than once. Pay
careful attention to question being asked.
Consider what a realistic solution might look
2. Assign a variable for value being sought.
Express other quantities in terms of this
3. List all known facts, as math expressions.
These may be eqns involving the variable.
Draw labeled diagram, table or chart it might
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
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
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?
Do problems for 1.1