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Chapter
Chapter3
2
Solving Equations
and Problem
Solving
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Slide 1
Section 3.4
Solving Linear
Equations in One
Variable and
Problem Solving
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Slide 2
Addition
Subtraction Multiplication Division
sum
difference
product
quotient
plus
minus
times
divided
added to
subtracted
from
less than
multiply
shared equally
among
twice
per
increased by decrease by
of
divided by
total
twice/double/
triple
divided into
more than
less
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Slide 3
Example
Write each phrase as an algebraic expression. Use x
to represent “a number.”
a. 8 increased by a number
b. the quotient of a number and 7
c. the sum of 10 and twice a number
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Slide 4
Writing Sentences as Equations
Write each sentence as an equation. Use x to
represent “a number.”
a. 8 increased by a number is 12.
b. Twice a number equals negative 12.
c. The quotient of twice a number and 12 is equal
to 15.
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Slide 5
Using Problem-Solving Steps to Solve
Problems
UNDERSTAND the problem.
2. CHOOSE a variable to represent the unknown.
Use this variable to represent any other
unknowns.
TRANSLATE the problem into an equation.
3. SOLVE the equation.
4. STATE the results: Check the proposed solution
in the stated problem and state your conclusion.
1.
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Slide 6
Example
Twice a number plus 3 is the same as the number
minus 6. Find the number.
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Slide 7
Example
The distance by road from Chicago to Los Angeles is 1091
miles more than the distance from Chicago to Boston. If the
total of these two distances is 3017 miles, find the distance
from Chicago to Boston.
continued
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Slide 8
Example
A woman’s $57,000 estate is to be divided so that
her husband receives twice as much as her son.
How much will each receive?
Copyright © 2015, 2011, 2008 Pearson Education, Inc.
Slide 9