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Know it for Alg 1
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Copyright by Holt, Rinehart and Winston. 45 Algebra 1All rights reserved.
3-1 Graphing and Writing Inequalities
Write the inequality shown by each graph.
1.
2.
3.
Graph each inequality.
4. r 1
5. g 22
3-2 Solving Inequalities by Adding and Subtracting
Solve each inequality and graph the solutions.
6. 4 t 3
7. r 7 12
8. Danny must have at least 410 points to receive an A. He has 275 points.Write and solve an inequality to show the least number of points Dannyneeds to receive an A.
4 2 2 40
4 2 2 40
4 2 2 40
Chapter Review3
CHAPTER
Copyright by Holt, Rinehart and Winston. 45 Algebra 1All rights reserved.
3-1 Graphing and Writing Inequalities
Write the inequality shown by each graph.
1.
2.
3.
Graph each inequality.
4. r 1
5. g 22
3-2 Solving Inequalities by Adding and Subtracting
Solve each inequality and graph the solutions.
6. 4 t 3
7. r 7 12
8. Danny must have at least 410 points to receive an A. He has 275 points.Write and solve an inequality to show the least number of points Dannyneeds to receive an A.
p 275 410; p 135; Danny needs at least 135 points to get an A.
4 28 6 2 4 6 80
4 28 6 2 4 6 80
4 2 2 40
4 2 2 40
k 04 2 2 40
y 24 2 2 40
t 54 2 2 40
t 7;
r 5;
Chapter Review3
CHAPTER
Copyright by Holt, Rinehart and Winston. 46 Algebra 1All rights reserved.
3-3 Solving Inequalities by Multiplying and Dividing
Solve each inequality and graph the solutions.
9. 3k
2
10. 3 h2
11. 2r 6
12. Hannah wants to buy 4 presents for at least $60. She wants to spend anequal amount of money on each present. Write and solve an inequality toshow the least amount of money Hannah will spend on each present.
3-4 Solving Two-Step and Multi-Step Inequalities
Solve each inequality.
13. c 3c 2 14 14. 23 12 2r 12r
15. 14 6 22f
16. 13b 12
56
Solve each inequality and graph the solutions.
17. 5a 2 22
18. 13 2t 3(t 3)
CHAPTER 3 REVIEW CONTINUED
Copyright by Holt, Rinehart and Winston. 46 Algebra 1All rights reserved.
3-3 Solving Inequalities by Multiplying and Dividing
Solve each inequality and graph the solutions.
9. 3k
2
10. 3 h2
11. 2r 6
12. Hannah wants to buy 4 presents for at least $60. She wants to spend anequal amount of money on each present. Write and solve an inequality toshow the least amount of money Hannah will spend on each present.
3-4 Solving Two-Step and Multi-Step Inequalities
Solve each inequality.
13. c 3c 2 14 14. 23 12 2r 12r
15. 14 6 22f
16. 13b 12
56
Solve each inequality and graph the solutions.
17. 5a 2 22
18. 13 2t 3(t 3)
4 28 6 2 4 6 8 0
4 28 6 2 4 6 8 0
b 4f 11
r 2c 4
4x 60; x 15; Each present will cost at least $15.
4 28 6 2 4 6 8 0
4 28 6 2 4 6 8 0
4 28 6 2 4 6 8 0
k 6;
h 6;
r 3;
a 4;
t 4;
CHAPTER 3 REVIEW CONTINUED
Copyright by Holt, Rinehart and Winston. 47 Algebra 1All rights reserved.
3-5 Solving Inequalities with Variables on Both Sides
Solve each inequality.
19. 12(3 8t) 20(1 15t) 20. 2(4 a) 2 2a 6
Solve each inequality and graph the solutions.
21. 4(3m 1) 2(m 3)
22. 9d 4 12 5d
23. The booster club raised $104 to buy soccer balls for the soccer team. Each soccer ball costs $19. How many soccer balls can the booster club buy?
3-6 Solving Compound Inequalities
Solve each compound inequality and graph the solutions.
24. 4 r 5 1
25. 4v 3 5 or 2v 7 1
Write the compound inequality shown by each graph.
26.
27.4 2 2 40
4 2 2 40
CHAPTER 3 REVIEW CONTINUED
Copyright by Holt, Rinehart and Winston. 47 Algebra 1All rights reserved.
3-5 Solving Inequalities with Variables on Both Sides
Solve each inequality.
19. 12(3 8t) 20(1 15t) 20. 2(4 a) 2 2a 6
Solve each inequality and graph the solutions.
21. 4(3m 1) 2(m 3)
22. 9d 4 12 5d
23. The booster club raised $104 to buy soccer balls for the soccer team. Each soccer ball costs $19. How many soccer balls can the booster club buy?
3-6 Solving Compound Inequalities
Solve each compound inequality and graph the solutions.
24. 4 r 5 1
25. 4v 3 5 or 2v 7 1
Write the compound inequality shown by each graph.
26.
27.4 k 2
4 2 2 40
x 0 OR x 04 2 2 40
4 28 6 2 4 6 8 0
4 28 6 2 4 6 8 0
They can buy no more than 5 soccer balls.
4 28 6 2 4 6 8 0
4 28 6 2 4 6 8 0
all real numbersno solutions
m 1;
d 4;
1 r 4;
v 2 OR v 3;
CHAPTER 3 REVIEW CONTINUED
Copyright by Holt, Rinehart and Winston. 48 Algebra 1All rights reserved.
CHAPTER 3 REVIEW CONTINUED
3-7 Solving Absolute-Value Inequalities
Solve each inequality.
28. x 3 5 29. 3a 9 2
Solve each absolute-value inequality and graph the solutions.
30. x 3 2 31. x 2 2.8 3.2
Write an absolute-value inequality for each graph.
32.
33.
Tell whether the given value of x is a solution of the inequality.
34. x 4; x 6
2 3 4 51012345
2 3 4 51012345
Copyright by Holt, Rinehart and Winston. 48 Algebra 1All rights reserved.
CHAPTER 3 REVIEW CONTINUED
3-7 Solving Absolute-Value Inequalities
Solve each inequality.
28. x 3 5 29. 3a 9 2
Solve each absolute-value inequality and graph the solutions.
30. x 3 2 31. x 2 2.8 3.2
Write an absolute-value inequality for each graph.
32.
33.
Tell whether the given value of x is a solution of the inequality.
34. x 4; x 6yes
x 3.52 3 4 51012345
x 12 3 4 51012345
8 x 4x 1 OR x 5
all real numbers
0 1 2 31234567 4 6 8 1020246810
Big Ideas3
CHAPTER
Copyright by Holt, Rinehart and Winston. 49 Algebra 1All rights reserved.
Answer these questions to summarize the important concepts fromChapter 3 in your own words.
1. Explain how to show that an endpoint is a solution. Explain how to showthat an endpoint is not a solution.
2. Explain how solving a one-step or multi-step inequality is like solving aone-step or multi-step equation.
3. Explain how solving inequalities by multiplying or dividing by a negativenumber is different from solving inequalities by multiplying or dividing by apositive number.
4. Explain how to graph a compound inequality involving a union
5. Describe how to use an absolute-value inequality to find all the values on anumber line that are within 3 units of 1.
For more review of Chapter 3: Complete the Chapter 3 Study Guide and Review on pages 186189 of
your textbook. Complete the Ready to Go On quizzes on pages 155 and 185 of your
textbook.
Big Ideas3
CHAPTER
Copyright by Holt, Rinehart and Winston. 49 Algebra 1All rights reserved.
Answer these questions to summarize the important concepts fromChapter 3 in your own words.
1. Explain how to show that an endpoint is a solution. Explain how to showthat an endpoint is not a solution.
2. Explain how solving a one-step or multi-step inequality is like solving aone-step or multi-step equation.
3. Explain how solving inequalities by multiplying or dividing by a negativenumber is different from solving inequalities by multiplying or dividing by apositive number.
4. Explain how to graph a compound inequality involving a union
5. Describe how to use an absolute-value inequality to find all the values on anumber line that are within 3 units of 1.
For more review of Chapter 3: Complete the Chapter 3 Study Guide and Review on pages 186189 of
your textbook. Complete the Ready to Go On quizzes on pages 155 and 185 of your
textbook.
The difference between a number and 1 must be less than 3.x (1) 3, or x 1 3
Graph each part of the inequality separately noting when to use asolid circle and when to use an empty circle.
When you multiply or divide both sides of an inequality by thesame negative number, you reverse the inequality symbol. Whenyou multiply or divide both sides of an inequality by the samepositive number, you do not change the inequality symbol.
To solve an inequality or an equation, you need to isolate thevariable and use inverse operations.
To show that an endpoint is a solution, draw a solid circle at thenumber. To show that an endpoint is not a solution, draw an emptycircle.