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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