1-5 Solving Inequalities
Solve each inequality. Then graph the solution set on a number line.
11. SOLUTION: To graph this inequality, draw a solid circle at -3 and draw an arrow extending to the left.
13. SOLUTION: To graph this inequality, draw a solid circle at
and draw an arrow extending to the left.
15. SOLUTION: To graph this inequality, draw an open circle at 27 and draw an arrow extending to the left.
17. SOLUTION: eSolutions Manual - Powered by Cognero
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To graph this inequality, draw an open circle at 27 and draw an arrow extending to the left.
1-5 Solving Inequalities
17. SOLUTION: To graph this inequality, draw an open circle at 3 and draw an arrow extending to the left.
19. SOLUTION: To graph this inequality, draw an open circle at 1 and draw an arrow extending to the left.
21. SOLUTION: eSolutions Manual - Powered by Cognero
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To graph this inequality, draw an open circle at 1 and draw an arrow extending to the left.
1-5 Solving Inequalities
21. SOLUTION: To graph this inequality, draw an open circle at 3 and draw an arrow extending to the left.
Define a variable and write an inequality for each problem. Then solve.
23. Twelve less than the product of three and a number is less than 21.
SOLUTION: Let x be the unknown number.
25. The difference of 5 times a number and 6 is greater than the number.
SOLUTION: Let x be the unknown number.
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1-5 Solving Inequalities
25. The difference of 5 times a number and 6 is greater than the number.
SOLUTION: Let x be the unknown number.
27. HIKING Danielle can hike 3 miles in an hour, but she has to take a one-hour break for lunch and a one-hour break
for dinner. If Danielle wants to hike at least 18 miles, solve
to determine how many hours the hike
should take.
SOLUTION: Danielle has to hike for at least 8 hours.
Solve each inequality. Then graph the solution set on a number line.
29. SOLUTION: To graph this inequality, draw an open circle at
and draw an arrow extending to the right.
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1-5 Solving
Inequalities
Danielle has to hike for at least 8 hours.
Solve each inequality. Then graph the solution set on a number line.
29. SOLUTION: To graph this inequality, draw an open circle at
and draw an arrow extending to the right.
31. SOLUTION: To graph this inequality, draw an open circle at 18.75 and draw an arrow extending to the right.
33. SOLUTION: To graph this inequality, draw an open circle at –4.5 and draw an arrow extending to the right.
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To graph this inequality, draw an open circle at 18.75 and draw an arrow extending to the right.
1-5 Solving Inequalities
33. SOLUTION: To graph this inequality, draw an open circle at –4.5 and draw an arrow extending to the right.
35. SOLUTION: To graph this inequality, draw an open circle at
and draw an arrow extending to the right.
47. CHALLENGE Given
that
exists.
with sides and
, determine the values of x such
SOLUTION: Using the Triangle Inequality Theorem, we know that the sum of the lengths of any 2 sides of a triangle must be
greater than the length of the remaining side. This generates 3 inequalities to examine.
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To graph this inequality, draw an open circle at
and draw an arrow extending to the right.
1-5 Solving Inequalities
47. CHALLENGE Given
that
exists.
with sides and
, determine the values of x such
SOLUTION: Using the Triangle Inequality Theorem, we know that the sum of the lengths of any 2 sides of a triangle must be
greater than the length of the remaining side. This generates 3 inequalities to examine.
In order for all 3 conditions to be true, x must be greater than 0.2.
49. WRITING IN MATH Why does the inequality symbol need to be reversed when multiplying or dividing by a
negative number?
SOLUTION: Sample answer: When one number is greater than another number, it is either more positive or less negative than
that number. When these numbers are multiplied by a negative value, their roles are reversed. That is, the number
that was more positive is now more negative than the other number. Thus, it is now less than that number and the
inequality symbol needs to be reversed.
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51. STATISTICS The mean score for Samantha’s first six algebra quizzes was 88. If she scored a 95 on her next quiz,
what will her mean score be for all 7 quizzes?
A 89 C 91
1-5 Solving
Inequalities
In order for all 3 conditions to be true, x must be greater than 0.2.
49. WRITING IN MATH Why does the inequality symbol need to be reversed when multiplying or dividing by a
negative number?
SOLUTION: Sample answer: When one number is greater than another number, it is either more positive or less negative than
that number. When these numbers are multiplied by a negative value, their roles are reversed. That is, the number
that was more positive is now more negative than the other number. Thus, it is now less than that number and the
inequality symbol needs to be reversed.
51. STATISTICS The mean score for Samantha’s first six algebra quizzes was 88. If she scored a 95 on her next quiz,
what will her mean score be for all 7 quizzes?
A 89 C 91
B 90 D 92
SOLUTION: Let x be the sum of the scores of first six algebra quizzes.
So, the correct choice is A.
53. What is the complete solution of the equation
A x = 8; x = 12
B x = 8; x = –12
C x = –8; x = –12
D x = –8; x = 12
?
SOLUTION: Check:
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1-5 Solving
Inequalities
So, the correct choice is A.
53. What is the complete solution of the equation
A x = 8; x = 12
B x = 8; x = –12
C x = –8; x = –12
D x = –8; x = 12
?
SOLUTION: Check:
The solution set is
.
So, the correct choice is D.
Solve each equation. Check your solutions.
55. SOLUTION: eSolutions Manual - Powered by Cognero
There appear to be two solutions,
.
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The solution
set is
.
1-5 Solving
Inequalities
So, the correct choice is D.
Solve each equation. Check your solutions.
55. SOLUTION: There appear to be two solutions,
.
Check: Substitute the values in the original equation.
The solution set is
.
57. ASTRONOMY Pluto travels in a path that is not circular. Pluto’s farthest distance from the Sun is 4539 million
miles, and its closest distance is 2756 million miles. Write an equation that can be solved to find the minimum and
maximum distances from the Sun to Pluto.
SOLUTION: Manual - Powered by Cognero
eSolutions
The value of c is 4539 – 891.5 or 3647.5.
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The solution
set is
1-5 Solving
Inequalities
.
57. ASTRONOMY Pluto travels in a path that is not circular. Pluto’s farthest distance from the Sun is 4539 million
miles, and its closest distance is 2756 million miles. Write an equation that can be solved to find the minimum and
maximum distances from the Sun to Pluto.
SOLUTION: The value of c is 4539 – 891.5 or 3647.5.
Substitute r = 891.5 and c = 3647.5 in the equation
.
.
59. GEOMETRY The formula for the surface area of a cylinder is
a. Use the Distributive Property to rewrite the formula by factoring out the greatest common factor of the two
terms.
b. Find the surface area for a cylinder with radius 3 centimeters and height 10 centimeters using both formulas.
Leave the answer in terms of .
c. Which formula do you prefer? Explain your reasoning.
SOLUTION: a.
The GCF of the two terms is 2πr.
b. Substitute r = 3 and h = 10 in the formula
.
Substitute r = 3 and h = 10 in the formula eSolutions Manual - Powered by Cognero
2
Therefore, the surface area of the cylinder is 78π cm .
c. Sample answer: The formula in part b is quicker.
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The value of c is 4539 – 891.5 or 3647.5.
Substitute r = 891.5 and c = 3647.5 in the equation
1-5 Solving Inequalities
.
.
59. GEOMETRY The formula for the surface area of a cylinder is
a. Use the Distributive Property to rewrite the formula by factoring out the greatest common factor of the two
terms.
b. Find the surface area for a cylinder with radius 3 centimeters and height 10 centimeters using both formulas.
Leave the answer in terms of .
c. Which formula do you prefer? Explain your reasoning.
SOLUTION: a.
The GCF of the two terms is 2πr.
b. Substitute r = 3 and h = 10 in the formula
.
Substitute r = 3 and h = 10 in the formula 2
Therefore, the surface area of the cylinder is 78π cm .
c. Sample answer: The formula in part b is quicker.
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