Unit 5bChapter 5

Algebraic Inequalities

Name ___________________________ Class___________

InequalitiesThe difference between an Equation and an Inequality is:

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What is this inequality? What is this inequality?

Graph each inequality:

x< 4 (A number less than 4)

x < 6 (A number less than or equal to 6)

x > –3 (A number greater than –3)

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Use the following symbols to represent inequalities:

_______ means “is less than.” _______ means “is less than or equal to.”

_______means “is greater than.” _______ means “is greater than or equal to.”

Practice

1. x < 3

2. x > –5

3. x < –1

4. x > 2

Solve Inequalities by Addition or SubtractionSolve each inequality.

1. p+9<7 2. t+6>−4

3. 7+b≤−12 4. −15+k>16

5. n−11>25 6. h−4>−8

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7. b−34< 12 8. f−5.2≥1.6

Solve each inequality. Graph the solution on a number line.

9. n+5<7 10. t+2>10

11. p−5>−4 12.13+n≥3

13. s− 34≤4 14. w−2.3>6.9

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Word Problems

Write an inequality and solve each problem.

1. Four more than a number is no more than thirteen.

2. The difference of a number and −¿6 is less than 9.

3. Eleven less than a number is more than seventeen.

4. The sum of −¿8 and a number is at least 9.

5. ENVELOPES Sam has at least 68 envelopes to address. He has addressed 17 of them. Write and solve an inequality that describes how many more envelopes, at most, Sam has left to address.

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Inequalities with Multiplication or Division

Solve each inequality. Graph the solution set on a number line.

1. 8w ≤ –8 2. 6a > –66

3. 25t ≤ 500 4. 3g < –18

5.y4 ≤ 1.5 6.

r.5 < 24

7. k.25 < –8 8.

m8 ≤ 2.5

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Multiplying and Dividing Negative Coefficients

Solve t

−6≤−4 t

−6≤−4

Then graph the solution set on a number line.

Step 1: Write the inequality.Step 2: Multiply by –6 and reverse the inequality symbol.Step 3: Check the solution.

Solve −45x<20

1. −¿3a >−¿12 2. r

−2≤6

3. –6c ≥ 30 4. −23y< 12

5. −h5 < –10 8. −¿7a ≤ 42

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Two–Step Inequalities

1. 3x + 4 > 16 2. 5 + 4x < 33

3. 2x + 8 > 24 4.12x−5<−8

5.x2+9≥5 6. 5x – 7 > 43

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7. 11≤7+ x5 8.

34x+5<38

Two–Step Inequalities with Negative Coefficients

1. 7−2x>11 2. −4 x−2≤18

3. −4 x+8<24 4. 8− x3≤7

5. −3 x−4<−25 6. −2−x ≤3

7. −2 x−6>−12 8.−x2

−3≤−2

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9. −7>− x−2 10. – x3+1≤1

Mixed Practice

Solve and graph each inequality. Check your solution.

1. 13a + 26 ≥ –13 2. 3b – 9 > –24

3. –3m – 6 ≥ –2 4.c2 – 3 < –11

5. y

−3+4<1 6.

−13x+ 3 > –1

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Word Problems

1. A rental car company charges $45 plus $0.20 per mile to rent a car. Mr. Lawrence does not want to spend more than $100 for his rental car. Write and solve an inequality to find how many miles he can drive and not spend more $100.

2. Halfway through the bowling season, Stewart has 34 strikes. He averages 2 strikes per game. Write and solve an inequality to find how many more games it will take for Stewart to have at least 61 strike, the league record.

3. Mrs. Treble charges her music students $25 per lesson plus a recital fee of $50. How many lessons can the student take if she pays no more than $175?

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4. A rental company charges $15 plus $4 per hour to rent a bicycle. If Margie does not want to spend more than $27 for her rental,write and solve an inequality to find how many hours she can rent thebicycle and not spend more than $27. Interpret the solution.

ReviewSolve and graph the solution to each of the following.

1. 4 x –3<9 2. −2 x –1<– 11

3. −2+2 x>−16 4. −3 x+2≤17

5. 7< x2+4 6.

x−5 + 1 ≥ 2

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7. – 4≤4 x+8 8. –3 x –3>12

9. Randy is mowing grass to save money for a vacation.He charges $12 per yard. Randy already has $40 and wants to have atleast $148 to take with him. Write and solve an inequality to determinehow many yards Randy needs to mow to have at least $148.

10. The Recreation Center rents rooms for an hourly rate, plus a set–up fee.

a. A group has $140 to spend. The inequality 15h + 40 < 140 represents the cost to rent the main hall, where h represents the number of hours the group can rent the room. Solve the inequality.

b. The same group also is considering renting the dining room. Write and solve an inequality to represent this situation.

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c. Which room should the group rent?

11. You can work at most 24 hours per week as a nurse’s aide. So far this week you have work 7 hours. If the remaining shifts are each 4 hours long, how many possible full shifts can you work?

12. Debbie has at most $60 to spend on clothes. She wants to buy a pair of jeans for $22 and spend the rest on t–shirts. Each t–shirt cost $8. Write and inequality and solve for the number of t–shirts Debbie can buy.

13. Clay budgeted $10 to treat his friend to snacks at the movies. Drinks cost $1.50 each, and a box of popcorn costs $1.75. How many drinks can he buy for him and his friends if he buys two boxes of popcorn?

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14. Dale has $25 to spend at a carnival. If the admission to the carnival is $4 and the rides cost $1.50 each, what is the greatest number of carnival rides Dale can go on?

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