Slide 1Copyright © 2015, 2011, 2008 Pearson Education, Inc.

Chapter 2

Solving Equations and Problem Solving

Chapter 3

Slide 2Copyright © 2015, 2011, 2008 Pearson Education, Inc.

Solving Linear Equations in One

Variable and Problem Solving

Section 3.4

Slide 3Copyright © 2015, 2011, 2008 Pearson Education, Inc.

Addition Subtraction Multiplication Division

sum difference product quotient

plus minus times divided

added to subtracted from

multiply shared equally among

more than less than twice per

increased by decrease by of divided by

total less twice/double/triple

divided into

Slide 4Copyright © 2015, 2011, 2008 Pearson Education, Inc.

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

Slide 5Copyright © 2015, 2011, 2008 Pearson Education, Inc.

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.

Slide 6Copyright © 2015, 2011, 2008 Pearson Education, Inc.

Using Problem-Solving Steps to Solve Problems

1. 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.

Slide 7Copyright © 2015, 2011, 2008 Pearson Education, Inc.

Example

Twice a number plus 3 is the same as the number minus 6. Find the number.

Slide 8Copyright © 2015, 2011, 2008 Pearson Education, Inc.

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

Slide 9Copyright © 2015, 2011, 2008 Pearson Education, Inc.

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?