College Prep Unit 2: Equations and Inequalities College Prep

CollegePrep Unit2:EquationsandInequalities

Ms.Talhami 1

CollegePrepUnit2:EquationsandInequalities

Name_________________


Ms.Talhami 2

HelpfulVocabularyWord Definition/Explanation Examples/HelpfulTips


Ms.Talhami 3

LiteralEquationsVocabulary Definition Examples

LiteralEquation

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Worksheet by Kuta Software LLC

Kuta Software - Infinite Algebra 1

Literal Equations

Name___________________________________

Date________________ Period____

Solve each equation for the indicated variable.

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3) z� �m��x , for x 4) g� �ca , for a

5) u� �x��k , for x 6) g� �c��x , for x

7) u� �ka

, for a8) g� �xc , for x

9) ��am� �� , for a 10) ��x��c� �� , for x

11) am� �n��p , for a12) u� �

akb

, for a

13) a��c� �d ��r , for a 14) xm� �np , for x


Ms.Talhami 4

SolvingInequalitiesVocabulary Definition Examples

Inequality

TheFourInequalitySymbols

< ≤ > ≥

Whathappenswhenyoumultiplyordividebyanegative?a)15 > 5 b)−4 < −1 c)8 < 10 d)−9 > −12

Name :Teacher : Date :

Score :

Math-Aids.Com

Write the Correct Comparison Symbol ( >, < or = ) in Each Box

1 ) -95 -89

2 ) 225 222

3 ) 18 47

4 ) -70 -23

5 ) -15 -77

6 ) -984 -860

7 ) 578 324

8 ) 92 40

9 ) -57 -68

10 ) -881 -555

11 ) 63 35

12 ) 863 730

13 ) -286 -598

14 ) 720 261

15 ) 483 957

16 ) 341 657

17 ) -15 -96

18 ) 74 10

19 ) -47 -49

20 ) -490 -612


Ms.Talhami 5

GraphInequalitiesonaNumberLine

<

>

≤

≥

Name :Teacher : Date :

Score :

Math-Aids.Com

Graphing InequalitiesGraphing Inequalities1 ) m< >|

0|1

|2

|3

|4

|5

|6

|7

|8

|9

|10

|11

|12

|13

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>o2 ) v< >| |

-3| |

-2| |

-1| |

0| |

1| |

2| |

3|< o

3 ) s< >|

-7|

-6|

-5|

-4|

-3|

-2|

-1|0

|1

|2

|3

|4

|5

|6

|7

< o4 ) w< >|

0|1

|2

|3

|4

|5

|6

|7

|8

|9

|10

|11

|12

|13

|14

< o5 ) n< >| |

-3| |

-2| |

-1| |

0| |

1| |

2| |

3| >o

6 ) w 5< >|

0|1

|2

|3

|4

|5

|6

|7

|8

|9

|10

|11

|12

|13

|14

7 ) - b 5< >|

-7|

-6|

-5|

-4|

-3|

-2|

-1|0

|1

|2

|3

|4

|5

|6

|7

8 ) f 12< >|

0|1

|2

|3

|4

|5

|6

|7

|8

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|10

|11

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9 ) 0.5 - f< >| |

-3| |

-2| |

-1| |

0| |

1| |

2| |

3|

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0|1

|2

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-7|

-6|

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|1

|2

|3

|4

|5

|6

|7

12 ) m< >| |

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0| |

1| |

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3|< o

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< o16 ) f< >|

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|2

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|10

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|12

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>o17 ) 3 g< >| |

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-1| |

0| |

1| |

2| |

3|

18 ) 8 d< >|

0|1

|2

|3

|4

|5

|6

|7

|8

|9

|10

|11

|12

|13

|14

19 ) - m -1< >|

-7|

-6|

-5|

-4|

-3|

-2|

-1|0

|1

|2

|3

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|6

|7

20 ) - n 1< >|

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-6|

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Ms.Talhami 6

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Kuta Software - Infinite Algebra 2 Name___________________________________

Period____Date________________Solving Inequalities

Solve each inequality and graph its solution.

1) 0 >

3

x

− 3 − 6

−2 −1 0 1 2 3 4 5 6 7 8

2)

4

x

+ 1 − 1 ≥ −8

−5 −4 −3 −2 −1 0 1

3) −1 ≤

2

n

+ 4 − 5

−2 −1 0 1 2 3 4

4) −6 >

5

n

+ 5 + 4

−7 −6 −5 −4 −3 −2 −1 0 1 2

5) 0 ≤

2

n

+ 3

n

−5 −4 −3 −2 −1 0 1 2

6)

2

p

− 4

p

≤ −2

−4 −3 −2 −1 0 1 2 3 4 5

7) 7 <

−(

−

k

− 3) + 2

−3 −2 −1 0 1 2 3 4

8)

3 −

2(

n

− 4) > −1

3 4 5 6 7 8

9)

−5(

1 − 4

a

) > −5

−4 −3 −2 −1 0 1 2 3 4

10)

−2(

b

+ 1) + 4 < 10

−8 −7 −6 −5 −4 −3 −2 −1 0 1

-1-


Ms.Talhami 7

True,False,orOpenSentenceTypeofSentence Examples

TrueSentence

FalseSentence

OpenSentence

Classifyeachsentenceastrue,false,oropen.

a.9 − 1 < 8 b.5 > 2 + 3 c.12 < 4 − 𝑥d.40 ≥ (10)(4) e.𝑥 + 2 = 7 f.– 1 − 12 = 11g.14 + 6 = 20 h.𝑥 + 23 < 10 i.24 + 3𝑥 = (8 + 𝑥)7Conjunctionvs.Disjunction

Vocabulary Definition Examples

Conjunction

Symbol:∧

Disjunction

Symbol:∨

Statewhethereachsentenceistrue,false,oropen.

a.3 + 2 = 5𝑎𝑛𝑑5 − 7 = −2 b.– 5 − 10 > 0𝑜𝑟4 − 8 = 12c.17 − 𝑥 = 23𝑜𝑟1 + 2 = 3 d.9 − −4 < 9 − 4𝑎𝑛𝑑 − 3 > 0e.Marsisaplanet𝑎𝑛𝑑3 + 4 = 8 f.0 < −5𝑜𝑟0 > −(2 − 3)


Ms.Talhami 8

GraphingBasicCompoundInequalities

Name : Score :

Printable Math Worksheets @ www.mathworksheets4kids.com

Graph the compound inequalities.

−4 < x ≤ 43)

-1 0 1 2 3 4-2-3-4-5-6 5 6

5)

-2 0 2 4 6 8-4-6-8-10-12 10 12

7)

-1 0 1 2 3 4-2-3-4-5-6 5 6

9)

0 5 10 15 2520-10-15 -5-20-25-30 30

x ≤ 0 or x > 21)

-1 0 1 2 3 4-2-3-4-5-6 5 6

x > −1 and x < 32)

-1 0 1 2 3 4-2-3-4-5-6 5 6

4)

-1 0 1 2 3 4-2-3-4-5-6 5 6

6)

-3 0 3 6 9 12-6-9-12-15-18 15 18

8)

10)

-1 0 1 2 3 4-2-3-4-5-6 5 6

x ≥ 5 or x ≤ −6

10 > x > −8 x < 9 and x ≥ 3

x ≤ −2 and x ≥ −5 x ≥ 12 or x < −16

-4 0 4 8 12 16-8-12-16-20-24 20 24

x > 10 and x < 20 −3 ≤ x < 1

Graphing Compound Inequalities


Ms.Talhami 9

SolvingCompoundInequalities

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Period____Date________________Compound InequalitiesSolve each compound inequality and graph its solution.

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Ms.Talhami 10

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Period____Date________________Compound InequalitiesSolve each compound inequality and graph its solution.

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Ms.Talhami 11

AbsoluteValueReviewVocabulary Definition Examples

AbsoluteValue

Solveforx

a. 𝑥 = 5 b.− 𝑥 = −12 c. 𝑥 = 30SolvingBasicAbsoluteValueEquationsSolveandcheck.Ifanequationhasnosolution,stateso.

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Period____Date________________Solving Absolute Value Equations

Solve each equation.

1)

3

x = 9 2)

−3

r = 9

3)

b

5 = 1

4)

−6

m = 30

5)

n

3 = 2

6)

−4 + 5

x = 16

7)

−2

r − 1 = 11 8)

1 − 5

a = 29

9)

−2

n + 6 = 6 10)

v + 8 − 5 = 2

-1-


Ms.Talhami 12

MoreSolvingBasicAbsoluteValueEquationsSolveandcheck.Ifanequationhasnosolution,stateso.

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Period____Date________________Solving Absolute Value Equations


1)

3

x = 9 2)

−3

r = 9

3)

b

5 = 1

4)

−6

m = 30

5)

n

3 = 2

6)

−4 + 5

x = 16

7)

−2

r − 1 = 11 8)

1 − 5

a = 29

9)

−2

n + 6 = 6 10)

v + 8 − 5 = 2

-1-

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Period____Date________________Absolute Value Equations


1)

6

m = 42 2)

−6

x = 30

3)

k − 10 = 34)

x

7 = 3

5)

7 +

p = 7 6)

−3

p = 15

7)

7

n = 568)

m

5 = 3

9)

−3

p = −12 10)

m + 2 = 11

11)

n + 1 = 212)

x

7 = 5

13)

a − 5

8 = 5

14)

4

n + 8 = 56

15)

7

m + 3 = 7316)

x

7 − 8 = −7

17)

−9 +

v

8 = 3

18)

−10

v + 2 = −70


Ms.Talhami 13

SolvingAbsoluteValueEquationswithVariablesonBothSidesSolveandcheck.Ifanequationhasnosolution,stateso.1) 4𝑥 + 3 = 3 − 𝑥 2) 𝑥 − 2 = 3𝑥 + 1

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Period____Date________________Absolute Value Equations


1)

6

m = 42 2)

−6

x = 30

3)

k − 10 = 34)

x

7 = 3

5)

7 +

p = 7 6)

−3

p = 15

7)

7

n = 568)

m

5 = 3

9)

−3

p = −12 10)

m + 2 = 11

11)

n + 1 = 212)

x

7 = 5

13)

a − 5

8 = 5

14)

4

n + 8 = 56

15)

7

m + 3 = 7316)

x

7 − 8 = −7

17)

−9 +

v

8 = 3

18)

−10

v + 2 = −70


Ms.Talhami 14

SolvingBasicAbsoluteValueInequalitiesSolvethefollowinginequalitiesandgraphthesolutionset.a. 𝑥 < 5 b. 𝑚 > 8c. 𝑦 ≤ 3 d. 𝑎 ≥ 7SolvingAbsoluteValueInequalities

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Period____Date________________Absolute Value InequalitiesSolve each inequality and graph its solution.

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Ms.Talhami 15

MoreSolvingAbsoluteValueInequalities

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Ms.Talhami 16

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College Prep Unit 2: Equations and Inequalities College Prep

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Transcript of College Prep Unit 2: Equations and Inequalities College Prep