Solved: Weight Loss Program A person enrolls in a diet and exercise program that

Fill in the blanks. The set of all real numbers that are solutions to an inequality is the ________ ________ of the inequality.

Fill in the blanks. The set of all points on the real number line that represent the solution set of an inequality is the ________ of the inequality.

Fill in the blanks. To solve a linear inequality in one variable, you can use the properties of inequalities, which are identical to those used to solve equations, with the exception of multiplying or dividing each side by a ________ number.

Fill in the blanks. Two inequalities that have the same solution set are ________ ________.

Fill in the blanks. It is sometimes possible to write two inequalities as one inequality, called a ________ inequality.

Fill in the blanks. The symbol _ is called a ________ symbol and is used to denote the combining of two sets.

In Exercises 712,match the inequality with its graph. [The graphs are labeled (a), (b), (c), (d), (e), and (f).]

In Exercises 712,match the inequality with its graph. [The graphs are labeled (a), (b), (c), (d), (e), and (f).]

In Exercises 712,match the inequality with its graph. [The graphs are labeled (a), (b), (c), (d), (e), and (f).]

In Exercises 712,match the inequality with its graph. [The graphs are labeled (a), (b), (c), (d), (e), and (f).]

In Exercises 712,match the inequality with its graph. [The graphs are labeled (a), (b), (c), (d), (e), and (f).]

In Exercises 712,match the inequality with its graph. [The graphs are labeled (a), (b), (c), (d), (e), and (f).]

In Exercises 1318, determine whether each value of is a solution of the inequality. (a) (b) (c) (d)

In Exercises 1318, determine whether each value of is a solution of the inequality. (a) (b) (c) (d) Inequality Values

In Exercises 1318, determine whether each value of is a solution of the inequality. (a) (b) (c) (d)

In Exercises 1318, determine whether each value of is a solution of the inequality. (a) (b) (c) (d)

In Exercises 1318, determine whether each value of is a solution of the inequality. (a) (b) (c) (d)

In Exercises 1318, determine whether each value of is a solution of the inequality. (a) (b) (c) (d)

In Exercises 1944, solve the inequality and sketch the solution on the real number line. (Some inequalities have no solutions.)

In Exercises 1944, solve the inequality and sketch the solution on the real number line. (Some inequalities have no solutions.)

In Exercises 1944, solve the inequality and sketch the solution on the real number line. (Some inequalities have no solutions.)

In Exercises 1944, solve the inequality and sketch the solution on the real number line. (Some inequalities have no solutions.)

In Exercises 1944, solve the inequality and sketch the solution on the real number line. (Some inequalities have no solutions.)

In Exercises 1944, solve the inequality and sketch the solution on the real number line. (Some inequalities have no solutions.)

In Exercises 1944, solve the inequality and sketch the solution on the real number line. (Some inequalities have no solutions.)

In Exercises 1944, solve the inequality and sketch the solution on the real number line. (Some inequalities have no solutions.)

In Exercises 1944, solve the inequality and sketch the solution on the real number line. (Some inequalities have no solutions.)

In Exercises 1944, solve the inequality and sketch the solution on the real number line. (Some inequalities have no solutions.)

In Exercises 1944, solve the inequality and sketch the solution on the real number line. (Some inequalities have no solutions.)

In Exercises 1944, solve the inequality and sketch the solution on the real number line. (Some inequalities have no solutions.)

In Exercises 1944, solve the inequality and sketch the solution on the real number line. (Some inequalities have no solutions.)

In Exercises 1944, solve the inequality and sketch the solution on the real number line. (Some inequalities have no solutions.)

In Exercises 1944, solve the inequality and sketch the solution on the real number line. (Some inequalities have no solutions.)

In Exercises 1944, solve the inequality and sketch the solution on the real number line. (Some inequalities have no solutions.)

In Exercises 1944, solve the inequality and sketch the solution on the real number line. (Some inequalities have no solutions.)

In Exercises 1944, solve the inequality and sketch the solution on the real number line. (Some inequalities have no solutions.)

In Exercises 1944, solve the inequality and sketch the solution on the real number line. (Some inequalities have no solutions.)

In Exercises 1944, solve the inequality and sketch the solution on the real number line. (Some inequalities have no solutions.)

In Exercises 1944, solve the inequality and sketch the solution on the real number line. (Some inequalities have no solutions.)

In Exercises 1944, solve the inequality and sketch the solution on the real number line. (Some inequalities have no solutions.)

In Exercises 1944, solve the inequality and sketch the solution on the real number line. (Some inequalities have no solutions.)

In Exercises 1944, solve the inequality and sketch the solution on the real number line. (Some inequalities have no solutions.)

In Exercises 1944, solve the inequality and sketch the solution on the real number line. (Some inequalities have no solutions.)

In Exercises 1944, solve the inequality and sketch the solution on the real number line. (Some inequalities have no solutions.)

In Exercises 4560, solve the inequality and sketch the solution on the real number line. (Some inequalities have no solution.)

In Exercises 4560, solve the inequality and sketch the solution on the real number line. (Some inequalities have no solution.)

In Exercises 4560, solve the inequality and sketch the solution on the real number line. (Some inequalities have no solution.)

In Exercises 4560, solve the inequality and sketch the solution on the real number line. (Some inequalities have no solution.)

In Exercises 4560, solve the inequality and sketch the solution on the real number line. (Some inequalities have no solution.)

In Exercises 4560, solve the inequality and sketch the solution on the real number line. (Some inequalities have no solution.)

In Exercises 4560, solve the inequality and sketch the solution on the real number line. (Some inequalities have no solution.)

In Exercises 4560, solve the inequality and sketch the solution on the real number line. (Some inequalities have no solution.)

In Exercises 4560, solve the inequality and sketch the solution on the real number line. (Some inequalities have no solution.)

In Exercises 4560, solve the inequality and sketch the solution on the real number line. (Some inequalities have no solution.)

In Exercises 4560, solve the inequality and sketch the solution on the real number line. (Some inequalities have no solution.)

In Exercises 4560, solve the inequality and sketch the solution on the real number line. (Some inequalities have no solution.)

In Exercises 4560, solve the inequality and sketch the solution on the real number line. (Some inequalities have no solution.)

In Exercises 4560, solve the inequality and sketch the solution on the real number line. (Some inequalities have no solution.)

In Exercises 4560, solve the inequality and sketch the solution on the real number line. (Some inequalities have no solution.)

In Exercises 4560, solve the inequality and sketch the solution on the real number line. (Some inequalities have no solution.)

In Exercises 6168, use a graphing utility to graph the inequality and identify the solution set.

In Exercises 6168, use a graphing utility to graph the inequality and identify the solution set.

In Exercises 6168, use a graphing utility to graph the inequality and identify the solution set.

In Exercises 6168, use a graphing utility to graph the inequality and identify the solution set.

In Exercises 6168, use a graphing utility to graph the inequality and identify the solution set.

In Exercises 6168, use a graphing utility to graph the inequality and identify the solution set.

In Exercises 6168, use a graphing utility to graph the inequality and identify the solution set.

In Exercises 6168, use a graphing utility to graph the inequality and identify the solution set.

In Exercises 6974, use a graphing utility to graph the equation.Use the graph to approximate the values of that satisfy each inequality.

In Exercises 6974, use a graphing utility to graph the equation.Use the graph to approximate the values of that satisfy each inequality.

In Exercises 6974, use a graphing utility to graph the equation.Use the graph to approximate the values of that satisfy each inequality.

In Exercises 6974, use a graphing utility to graph the equation.Use the graph to approximate the values of that satisfy each inequality.

In Exercises 6974, use a graphing utility to graph the equation.Use the graph to approximate the values of that satisfy each inequality.

In Exercises 6974, use a graphing utility to graph the equation.Use the graph to approximate the values of that satisfy each inequality.

In Exercises 7580, find the interval(s) on the real number line for which the radicand is nonnegative.

In Exercises 7580, find the interval(s) on the real number line for which the radicand is nonnegative.

In Exercises 7580, find the interval(s) on the real number line for which the radicand is nonnegative.

In Exercises 7580, find the interval(s) on the real number line for which the radicand is nonnegative.

In Exercises 7580, find the interval(s) on the real number line for which the radicand is nonnegative.

In Exercises 7580, find the interval(s) on the real number line for which the radicand is nonnegative.

Think About It The graph of can be described as all real numbers within three units of 5. Give a similar description of

Think About It The graph of can be described as all real numbers more than five units from 2. Give a similar description of

In Exercises 8390, use absolute value notation to define the interval (or pair of intervals) on the real number line.

In Exercises 8390, use absolute value notation to define the interval (or pair of intervals) on the real number line.

In Exercises 8390, use absolute value notation to define the interval (or pair of intervals) on the real number line.

In Exercises 8390, use absolute value notation to define the interval (or pair of intervals) on the real number line.

In Exercises 8390, use absolute value notation to define the interval (or pair of intervals) on the real number line. All real numbers within 10 units of 12

In Exercises 8390, use absolute value notation to define the interval (or pair of intervals) on the real number line. All real numbers at least five units from 8

In Exercises 8390, use absolute value notation to define the interval (or pair of intervals) on the real number line. All real numbers more than four units from

In Exercises 8390, use absolute value notation to define the interval (or pair of intervals) on the real number line. All real numbers no more than seven units from

Checking Account You can choose between two types of checking accounts at your local bank. Type A charges a monthly service fee of $6 plus $0.25 for each check written. Type B charges a monthly service fee of $4.50 plus $0.50 for each check written. How many checks must you write in a month in order for the monthly charges for type A to be less than that for type B?

Copying Costs Your department sends its copying to the photocopy center of your company. The center bills your department $0.10 per page. You have investigated the possibility of buying a departmental copier for $3000. With your own copier, the cost per page would be $0.03. The expected life of the copier is 4 years. How many copies must you make in the four-year period to justify buying the copier?

Investment In order for an investment of $1000 to grow to more than $1062.50 in 2 years, what must the annual interest rate be?

Investment In order for an investment of $750 to grow to more than $825 in 2 years, what must the annual interest rate be?

Cost, Revenue, and Profit The revenue for selling units of a product is The cost of producing units is To obtain a profit, the revenue must be greater than the cost. For what values of will this product return a profit?

Cost, Revenue, and Profit The revenue for selling units of a product is The cost of producing units is To obtain a profit, the revenue must be greater than the cost. For what values of will this product return a profit?

Daily Sales A doughnut shop sells a dozen doughnuts for $2.95. Beyond the fixed costs (rent, utilities, and insurance) of $150 per day, it costs $1.45 for enough materials (flour, sugar, and so on) and labor to produce a dozen doughnuts. The daily profit from doughnut sales varies between $50 and $200. Between what levels (in dozens) do the daily sales vary?

Weight Loss Program A person enrolls in a diet and exercise program that guarantees a loss of at least pounds per week. The persons weight at the beginning of the program is 164 pounds. Find the maximum number of weeks before the person attains a goal weight of 128 pounds.

Data Analysis: IQ Scores and GPA The admissions office of a college wants to determine whether there is a relationship between IQ scores and grade-point averages after the first year of school. An equation that models the data the admissions office obtained is (a) Use a graphing utility to graph the model. (b) Use the graph to estimate the values of that predict a grade-point average of at least 3.0.

Data Analysis: Weightlifting You want to determine whether there is a relationship between an athletes weight (in pounds) and the athletes maximum benchpress weight (in pounds). The table shows a sample of data from 12 athletes. (a) Use a graphing utility to plot the data. (b) A model for the data is Use a graphing utility to graph the model in the same viewing window used in part (a). (c) Use the graph to estimate the values of that predict a maximum bench-press weight of at least 200 pounds. (d) Verify your estimate from part (c) algebraically. (e) Use the graph to write a statement about the accuracy of the model. If you think the graph indicates that an athletes weight is not a particularly good indicator of the athletes maximum bench-press weight, list other factors that might influence an individuals maximum bench-press weight.

Teachers Salaries The average salary (in thousands of dollars) for elementary school teachers in the United States from 1990 to 2002 is approximated by the model where represents the year, with corresponding to 1990. (Source: National Education Association) (a) According to this model, when was the average salary at least $32,000, but not more than $42,000? (b) According to this model, when will the average salary exceed $48,000?

Egg Production The number of eggs (in billions) produced in the United States from 1990 to 2002 can be modeled by where represents the year, with corresponding to 1990. (Source: U.S. Department of Agriculture) (a) According to this model, when was the annual egg production 70 billion, but no more than 80 billion? (b) According to this model, when will the annual egg production exceed 95 billion?

Geometry The side of a square is measured as 10.4 inches with a possible error of inch. Using these measurements, determine the interval containing the possible areas of the square.

Geometry The side of a square is measured as 24.2 centimeters with a possible error of 0.25 centimeter. Using these measurements, determine the interval containing the possible areas of the square.

Accuracy of Measurement You stop at a self-service gas station to buy 15 gallons of 87-octane gasoline at $1.89 a gallon. The gas pump is accurate to within of a gallon. How much might you be undercharged or overcharged?

Accuracy of Measurement You buy six T-bone steaks that cost $14.99 per pound. The weight that is listed on the package is 5.72 pounds. The scale that weighed the package is accurate to within ounce. How much might you be undercharged or overcharged?

Time Study A time study was conducted to determine the length of time required to perform a particular task in a manufacturing process. The times required by approximately two-thirds of the workers in the study satisfied the inequality where is time in minutes. Determine the interval on the real number line in which these times lie.

Height The heights of two-thirds of the members of a population satisfy the inequality where is measured in inches. Determine the interval on the real number line in which these heights lie.

Meteorology An electronic device is to be operated in an environment with relative humidity in the interval defined by What are the minimum and maximum relative humidities for the operation of this device?

Music Michael Kasha of Florida State University used physics and mathematics to design a new classical guitar. He used the model for the frequency of the vibrations on a circular plate where is the frequency (in vibrations per second), is the plate thickness (in millimeters), is the diameter of the plate, is the elasticity of the plate material, and is the density of the plate material. For fixed values of and the graph of the equation is a line (see figure). (a) Estimate the frequency when the plate thickness is 2 millimeters. (b) Estimate the plate thickness when the frequency is 600 vibrations per second. (c) Approximate the interval for the plate thickness when the frequency is between 200 and 400 vibrations per second. (d) Approximate the interval for the frequency when the plate thickness is less than 3 millimeters. True or False?

True or False? In Exercises 111 and 112, determine whether the statement is true or false. Justify your answer. If and are real numbers, and then

True or False? In Exercises 111 and 112, determine whether the statement is true or false. Justify your answer. If then and

Identify the graph of the inequality (a) (b) (c) (d)

Find sets of values of and such that is a solution of the inequality _ax _ b_ c.