Math 123 – Section 2.7 – Solving Linear Inequalities – Part II
−
Page 1
© Copyright 2009 by John Fetcho. All rights reserved
Section 2.7
Linear Inequalities in One Variable – Part II
I. When solving word problems, remember to:
A. Define a variable for the unknown.
B. Write an equation/inequality expressing the situation.
C. Solve.
D. Answer the question with a complete sentence.
E. Examples - Solve each of the following.
1. The bar graph (top of right-hand column, page 184) shows the percentage of
wages full-time workers pay in income tax in eight selected countries. (The
percents shown are averages for single earners without children.) Let x
represent the percentage of wages workers pay in income tax. In Exercises
99-104, write the name of the country or countries described by the given
inequality.
x > 30% (#100)
We want to find all the countries greater than 30%, not included.
Answer: {Netherlands, Denmark}
2. Now you try one: 25% < x < 40% (#103)
Answer: {United States, Canada, Norway, Netherlands}
3. The line graph (middle of right-hand column, page 184) shows the declining
consumption of cigarettes in the United States. The data shown by the graph
can be modeled by
N = 550 – 9x
where N is the number of cigarettes consumed, in billions, x years after 1988.
Use this formula to solve Exercises 105 – 106.
Describe how many years after 1988 cigarette consumption will be less than
325 billion cigarettes per year. Which years are included in your description?
(#106)
Let N = 325 Remember that N is already measured in billions.
Let x = The number of years after 1988.
So x = 0 means 1988
x = 1 means 1989
x = 2 means 1990
x = 3 means 1991
etc.
So x = 17 means 2005
We now need to substitute in for N and write an inequality.
550 – 9x < 325 Subtract 550 from each side to isolate the variable term.
−9x < −225 Divide both sides by −9 to isolate the variable. Remember
to switch the inequality sign!
x > 25 Add to 1988 to determine the year.
