2.6 Solve Compound Inequalities

Solution sets joined by and versus or, where one demands an overlap and the other a union, plus three-part inequalities read as a single band.

Intermediate Algebra 2e, 2.6 Solve Compound Inequalities

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8 exercises

2.6 Exercise 1

Before you get started, take this readiness quiz.

Simplify: $\frac{2}{5} \left(x + 10\right) .$
If you missed this problem, review the reference.

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2.6 Exercise 2

Simplify: $− \left(x - 4\right) .$
If you missed this problem, review the reference.

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2.6 Exercise 22

Due to the drought in California, many communities now have tiered water rates. There are different rates for Conservation Usage, Normal Usage and Excessive Usage. The usage is measured in the number of hundred cubic feet (hcf) the property owner uses.

During the summer, a property owner will pay $24.72 plus $1.32 per hcf for Conservation Usage. The bill for Conservation Usage would be between or…

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2.6 Exercise 23

Due to the drought in California, many communities have tiered water rates. There are different rates for Conservation Usage, Normal Usage and Excessive Usage. The usage is measured in the number of hundred cubic feet (hcf) the property owner uses.

During the winter, a property owner will pay $24.72 plus $1.54 per hcf for Normal Usage. The bill for Normal Usage would be between or equal to $49.36…

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2.6 Exercise 75

Solve.

Gregory is thinking of a number and he wants his sister Lauren to guess the number. His first clue is that six less than twice his number is between four and forty-two. Write a compound inequality that shows the range of numbers that Gregory might be thinking of.

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2.6 Exercise 77

Solve.

Elouise is creating a rectangular garden in her back yard. The length of the garden is 12 feet. The perimeter of the garden must be at least 36 feet and no more than 48 feet. Use a compound inequality to find the range of values for the width of the garden.

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2.6 Exercise 79

Body Mass Index (BMI) is a measure of body fat is determined using your height and weight.

ⓐ Let x be your BMI. Research and then write the compound inequality to show the BMI range for you to be considered normal weight.

ⓑ Research a BMI calculator and determine your BMI. Is it a solution to the inequality in part (a)?

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2.6 Exercise 81

Explain the steps for solving the compound inequality $2 - 7 x \geq −5$ or $4 \left(x - 3\right) + 7 > 3 .$

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