Beginning Algebra, 11th Edition

75.For what values of xwould the rectangle
have a perimeter of at least 400?

76.For what values of xwould the triangle

have a perimeter of at least 72?

SECTION 2.8 Solving Linear Inequalities 161

EXERCISES 59–62

FOR INDIVIDUAL OR GROUP WORK

Work Exercises 59–62 in order,to see how the solutions of an inequality are closely

connected to the solution of the corresponding equation.

59.Solve the equation and graph the solution set on a number line.

60.Solve the inequality and graph the solution set on a number line.

61.Solve the inequality and graph the solution set on a number line.

62.If we were to graph all the solution sets from Exercises 59–61on the same number

line, describe the graph. (This is called the unionof all the solution sets.)

3 x+ 26 14,

3 x+ 27 14,

3 x+ 2 =14,

RELATING CONCEPTS

Concept Check Translate each statement into an inequality. Use x as the variable.

63.You must be at least 18 yr old to vote. 64.Less than 1 in. of rain fell.

65.Chicago received more than 5 in. of snow. 66.A full-time student must take at least
12 credits.

67.Tracy could spend at most $20 on a gift. 68.The car’s speed exceeded 60 mph.

Solve each problem. See Example 6.

69.Christy Heinrich has scores of 76 and 81 on her first two algebra tests. If she wants an
average of at least 80 after her third test, what possible scores can she make on that test?

70.Joseph Despagne has scores of 96 and 86 on his first two geometry tests. What possible
scores can he make on his third test so that his average is at least 90?

71.When 2 is added to the difference between six times a number and 5, the result is greater
than 13 added to five times the number. Find all such numbers.

72.When 8 is subtracted from the sum of three times a number and 6, the result is less than
4 more than the number. Find all such numbers.

73.The formula for converting Fahrenheit temperature to Celsius is

.

If the Celsius temperature on a certain winter day in Minneapolis is never less than

how would you describe the corresponding Fahrenheit temperatures? (Source:National

Climatic Data Center.)

74.The formula for converting Celsius temperature to Fahrenheit is

.

The Fahrenheit temperature of Phoenix has never exceeded How would you

describe this using Celsius temperature? (Source:National Climatic Data Center.)

122°.

F=

9

5

C+ 32

- 25°,

C=

5

9

1 F- 322

4 x + 3

x + 37

x + 11

2 x + 5

x