A student multiplied both sides of the inequality -1 3 x 4

Two or more expressions joined by an inequality sign is called a(n) _________.

a) a 6 b means that a is than b. b) a 7 b means that a is than b.

An inequality of the form a 6 x 6 b is called a(n) inequality.

When solving an inequality, if you obtain a statement that is always false, such as 3 7 5, the answer is solution.

When solving an inequality, if you obtain a statement that is always true, such as 2 7 1, the solution is real numbers.

When both sides of an inequality are multiplied or divided by a(n) number, the direction of the inequality symbol is reversed.

To indicate the solution set of x < 5 on the number line, we draw a(n) circle at 5.

To indicate the solution set of x 5 on the number line, we draw a(n) circle at 5.

In Exercises 926, graph the solution set of the inequality, where x is a real number, on the number line.x 5

In Exercises 926, graph the solution set of the inequality, where x is a real number, on the number line.x 6 3

In Exercises 926, graph the solution set of the inequality, where x is a real number, on the number line.x + 7 2

In Exercises 926, graph the solution set of the inequality, where x is a real number, on the number line.x - 4 7 -5

In Exercises 926, graph the solution set of the inequality, where x is a real number, on the number line.-3x 18

In Exercises 926, graph the solution set of the inequality, where x is a real number, on the number line.-4x 6 12

In Exercises 926, graph the solution set of the inequality, where x is a real number, on the number line.x 6 6 3

In Exercises 926, graph the solution set of the inequality, where x is a real number, on the number line.x 5 7 2

In Exercises 926, graph the solution set of the inequality, where x is a real number, on the number line.-x 3 3

In Exercises 926, graph the solution set of the inequality, where x is a real number, on the number line.-x 2 -4

In Exercises 9-26, graph the solution set of the inequality, where x is a real number, on the number line. 2x + 6 \(\geq\) 14

In Exercises 926, graph the solution set of the inequality, where x is a real number, on the number line.3x + 12 6 5x + 14

In Exercises 926, graph the solution set of the inequality, where x is a real number, on the number line.4(2x - 1) 6 2(4x - 3)

In Exercises 926, graph the solution set of the inequality, where x is a real number, on the number line.-2(x - 3) 4x + 6

In Exercises 926, graph the solution set of the inequality, where x is a real number, on the number line.-1 x 3

In Exercises 926, graph the solution set of the inequality, where x is a real number, on the number line.-4 6 x 1

In Exercises 926, graph the solution set of the inequality, where x is a real number, on the number line.2 6 x - 4 6

In Exercises 926, graph the solution set of the inequality, where x is a real number, on the number line.1 2 6 x + 4 2 4

In Exercises 2746, graph the solution set of the inequality, where x is an integer, on the number line.x 7 2

In Exercises 2746, graph the solution set of the inequality, where x is an integer, on the number line.-3 6 x

In Exercises 2746, graph the solution set of the inequality, where x is an integer, on the number line.-3x 27

In Exercises 2746, graph the solution set of the inequality, where x is an integer, on the number line.3x 27

In Exercises 2746, graph the solution set of the inequality, where x is an integer, on the number line.x - 4 6 -2

In Exercises 2746, graph the solution set of the inequality, where x is an integer, on the number line.x + 6 7 2

In Exercises 2746, graph the solution set of the inequality, where x is an integer, on the number line.x 3 -2

In Exercises 2746, graph the solution set of the inequality, where x is an integer, on the number line.x 4 -3

In Exercises 2746, graph the solution set of the inequality, where x is an integer, on the number line.- x 4 2

In Exercises 2746, graph the solution set of the inequality, where x is an integer, on the number line.3x 5 3

In Exercises 2746, graph the solution set of the inequality, where x is an integer, on the number line.-15 6 -4x - 3

In Exercises 2746, graph the solution set of the inequality, where x is an integer, on the number line.-5x - 1 6 17 - 2x

In Exercises 2746, graph the solution set of the inequality, where x is an integer, on the number line.3(x + 4) 4x + 13

In Exercises 2746, graph the solution set of the inequality, where x is an integer, on the number line.-2(x - 1) 6 3(x - 4) + 5

In Exercises 2746, graph the solution set of the inequality, where x is an integer, on the number line.5(x + 4) - 6 2x + 8

In Exercises 2746, graph the solution set of the inequality, where x is an integer, on the number line.-2 x 6

In Exercises 2746, graph the solution set of the inequality, where x is an integer, on the number line.1 7 -x 7 -6

In Exercises 27-46, graph the solution set of the inequality, where x is an integer, on the number line. -2<2 x+3<6

In Exercises 2746, graph the solution set of the inequality, where x is an integer, on the number line.0.3 x + 2 10 0.5

In Exercises 2746, graph the solution set of the inequality, where x is an integer, on the number line.-1 3 6 x - 2 12 1 4

Indianapolis 500 The following bar graph shows the average speed, in miles per hour (mph), of the winning driver of the Indianapolis 500 for the years 20042010. 160 150 140 130 2004 2005 2006 2007 2008 2010 2009 170 Average Speed of Winning Driver at Indianapolis 500 Year Speed (mph) 162 150 144 152 157 158 139 Source: indianapolismotorspeedway.com In which years was the average speed of the winning driver a) 7150 mph? b) 150 mph? c) 7160 mph? d) 140 mph?

Unemployment Rate The following graph shows the unemployment rate in the United States for the years 20012009. 8 7 9 6 4 3 5 2 1 0 2001 2002 2003 2004 2005 2006 2007 2008 2009 10 Unemployment Rate in the United States Year Percent 9.3 144 5.1 4.6 4.6 5.8 6.0 5.5 4.7 5.8 Source: U.S. Department of Labor In which years was the unemployment rate in the United States a) 7 5% b) 6 5.5% c) 5.5% d) 5.0%

DVD Rental Movie Mania offers two rental plans. One has an annual fee, and the other has no annual fee. The annual membership fee and the daily charge per DVD for each plan are shown in the table. Determine the maximum number of DVDs that can be rented for the no fee plan to cost less than the annual fee plan.

Salary Plans Bobby Exler recently accepted a sales position in Portland, Oregon. He can select between the two salary plans shown in the table. Determine the dollar amount of weekly sales that would result in Bobby earning more with Plan B than with Plan A.

College Employment To be eligible for financial assistance for college, Samantha Lavin can earn no more than $3200 during her summer employment. She will earn $662.50 cutting lawns. She is also earning $7.25 per hour at an evening job as a cashier at a grocery store. What is the maximum number of hours Samantha can work at the grocery store without jeopardizing her financial assistance?

Anniversary Patricia and Joe Kuby are celebrating their 75th wedding anniversary by having a party at the Diplomat Party House. They have budgeted $3000 for the party. If the party house charges a flat rate of $75 for set-up and clean-up, plus $25 per person, determine the maximum number of guests the Kubys can invite and remain within their budget.

Parking Costs A parking garage in Richmond, Virginia, charges $1.75 for the first hour and $0.50 for each additional hour or part of an hour. What is the maximum length of time Tom Shalhoub can park in the garage if he wishes to pay no more than $4.25?

Making a Profit For a business to realize a profit, its revenue, R, must be greater than its costs, C; that is, a profit will result only if R 7 C (the company breaks even when R = C). A dry cleaning store has a weekly cost equation of C = 0.25x + 1500 and a weekly revenue of R = 4x, where x is the number of garments dry cleaned in a week. How many garments must be dry cleaned in a week for the company to make a profit?

Finding Velocity The velocity, v, in feet per second, t sec after a tennis ball is projected directly upward is given by the formula v = 84 - 32t. How many seconds after being projected upward will the velocity be between 36 ft/sec and 68 ft/sec?

Speed Limit The minimum speed for vehicles on a highway is 40 mph, and the maximum speed is 55 mph. If Philip Rowe has been driving nonstop along the highway for 4 hr, what range in miles could he have legally traveled?

A Grade of B In Example 9 on page 332, what range of grades on the fifth test would result in Devon receiving a grade of B if his grades on the first four tests were 78%, 64%, 88%, and 76%?

Tent Rental The Cuhayoga Community College Planning Committee wants to rent tents for the spring job fair. Rent-a-Tent charges $325 for setup and delivery of its tents. This fee is charged regardless of the number of tents delivered and set up. In addition, Rent-a-Tent charges $125 for each tent rented. If the minimum amount the planning committee wishes to spend is $950 and the maximum amount they wish to spend is $1200, determine the minimum and maximum number of tents the committee can rent.

Painting a House Donovan Davis is painting the exterior of his house. The instructions on the paint can indicate that 1 gal covers from 250 to 400 ft2 . The total surface of the house to be painted is 2750 ft2 . Determine the number of gallons of paint he could use and express the answer as an inequality.

Final Exam Teresas five test grades for the semester are 86%, 78%, 68%, 92%, and 72%. Her final exam counts one-third of her final grade. What range of grades on her final exam would result in Teresa receiving a final grade of B in the course? (See Example 9.)

A student multiplied both sides of the inequality -1 3 x 4 by -3 and forgot to reverse the direction of the inequality symbol. What is the relation between the students incorrect solution set and the correct solution set? Is there any number in both the correct solution set and the students incorrect solution set? If so, what is it?

Find a newspaper or a magazine article that contains the mathematical concept of inequality. a) From the information in the article write a statement of inequality. b) Summarize the article and explain how you arrived at the inequality statement in part (a).