1. Equations and Inequalities
Chapter 2
Equations and Inequalities
2.1 – Solving Linear Equations
2.2 – Problem Solving and Using Formulas
2.3 – Applications of Algebra
2.4 – Additional Application Problems
2.5 – Solving Linear Inequalities
2.6 – Solving Equations and Inequalities Containing Absolute Values

2. 2.3 Applications of Algebra
Objectives:
1. Translate a Verbal Statement into an Algebraic Expression or Equation
2. Use the Problem-Solving Procedure for Solving Application Problems

3. Translate a Verbal Statement into an Algebraic Expression or Equation
Phrase
Algebraic Expression
A number increased by 8
x + 8
Twice a number 2x
7 less than a number
x – 7
One-ninth of a number
(1/9)x or x/9
2 more than 3 times a number
3x + 2
4 less than 6 times a number
6x – 4
12 times the sum of a number and 5
12(x + 5)

4. Solving Equations Example:
Express each phrase as an algebraic expression.
the radius, r, decreased by 9 centimeters
a) r – 9
b) 5 less than twice the distance, d
b) 2d – 5
c) 7 times a number, n, increased by 8
c)7n + 8

5. Use the Problem-Solving Procedure
Problem-Solving Procedure for Solving Application Problems
Understand the problem. Identity the quantity or quantities you are being asked to find.
Translate the problem into mathematical language (express the problems as an equation).
Carry out the mathematical calculations (solve the equation).
Check the answer (using the original wording of the problem).
Answer the question asked.

6. Solving Equations Example:
A Network offers its customers choices of several long-distance calling plans. The Nationwide Plan requires customers to pay a $5 monthly fee and 8 cents per minute for any long-distance calls made. The Flat Rate Unlimited Plan has a $25 monthly fee for unlimited calling—in other words, there is no per-minute fee. How many minutes of long-distance calls would a customer need to use for the two plans to cost the same amount?