Math 017 Materials With Exercises

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$Math 171 Review for the Final Exam$

$Math 171 Test 2$

$MATH 171 SYLLABUS$

■ Solve the following inequality x 5 x 3.This time, after subtracting x from each side we obtain5 3This is a false statement, false for all values of x . There is no value of x that would make thisstatement true. Thus x 3 x 5 has no solutions. ■Example 10.6 Solve the following inequality. 3(2x 5) 6xSolution: 3(2x 5) 6xRemove parentheses. 6x 15 6xAdd 6 x to both sides. 6x 15 6x 6x 6xSimplify. 15 0Since the obtained inequality 15 0 is always true, we conclude that all real numbers are solutionsof the inequality 3(2x 5) 6x.Common mistakes and misconceptionsMistake 10.1DO NOT forget to reverse the inequality sign any time you multiply or divide both sides of aninequality by a negative number.Mistake 10.2When solving an inequality DO NOT change the inequality sign to an equation sign.Mistake 10.3DO NOT forget to write the final answer. If you are getting 3 5 that means there is nosolution. You must write that there is „no solution‟. Likewise, if you get something like 5>3,which is true regardless of the value(s) of the variable(s), that means all numbers are solutions.You must write “all real numbers”.<strong>Exercises</strong> with Answers (For answers see Appendix A)Ex.1 List two numbers satisfying x 5 . List two numbers satisfying a 5. Is the second questiondifferent from the first one? How about asking: List two numbers satisfying 5 x ?Ex.2 Which of the following statements has the same meaning as x 2.a) 2 xb) 2 xc) x 2100
d) x 2and x 2e) All numbers x that are at least 2 .f) All numbers x that are no more than 2 .Ex.3 Name three numbers that satisfy the condition x 1Ex.4Find a number that satisfies2x but does not satisfy32x .3Ex.5 Circle all numbers that satisfy the following inequality x 3 3, 2 , 1, 0, 1, 2, 3, 4, 5Ex.6 Determine which of the following numbers do not satisfy the inequality x 3 3, 2 , 1, 0, 1, 2, 3, 4, 5Ex.7 Determine which of the following numbers satisfies the inequality x 0. 6 .1, .666, 6, 0.6 .5999,02Ex.8Describe the following sets of numbers using inequality signs.a) All negative numbers x .b) All non-positive numbers x .c) All numbers x that are at least equal to 6.d) All numbers x that are at most equal to 6.e) All numbers x that are not more than 6Ex.9 Graph the following sets on a number line provided. Assume that all marks on the line areequally spaced.a) x 4b)2x 13c) 4 xd) x 2e)f)4x 35x 2101
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Math 017MaterialsWithExercises
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TABLE OF CONTENTSLesson 1Variables
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Lesson 1___________________________
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e) „minus x ‟ or „the opposit
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For example,Evaluate 5 x when x 10
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3xd) x( y)e) 2f) 2x yz w(t)Ex.4 T
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Ex.16 Let x 3. Rewrite the express
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e) x5f) x2Ex.28 Substitute“undefi
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Lesson 2___________________________
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Solution:Please, notice the use of
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g)i)4( a 2)h)8y (x)4(ab)j) ( a d)
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1 2Ex.19 If possible, evaluate when
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Lesson 3___________________________
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Commutative Propertyof Additionx y
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2 x 2 xFor example, and thus als
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Example 3.10 Determine which of the
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Exercises with Answers (For answers
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Ex.16 Write the following expressio
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s) ( 0.2xy)( 0.3z)t)4x1Ex.24 Is 1
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Lesson 4___________________________
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Numerical coefficientsNumerical Coe
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For your convenience, we will displ
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9 818081a) 9 98097 6 76134 4 4 4
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Ex.8Simplify by raising to the indi
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73a 2xxi) 2aj)2( 42a)x(3xk)4x2 ) 3
Page 52 and 53: Lesson 5___________________________
Page 54 and 55: FactorizationThe Distributive Law l
Page 56 and 57: Simplification of algebraic fractio
Page 58 and 59: Mistake 5.1When factoring 3 from 3x
Page 60 and 61: Ex.13 Factor2a) 5 a from the follow
Page 62 and 63: 24x ( 5x)g)xa bi)7(a b)bc ( b e)
Page 64 and 65: Adding and subtracting like termsIf
Page 66 and 67: ) This should be written as 4x 2
Page 68 and 69: Ex.4 Circle all terms that are like
Page 70 and 71: 682 122k) 6 ( d a) a dl) 3a1(4a
Page 72 and 73: Lesson 7___________________________
Page 74 and 75: For instance, the area of a rectang
Page 76 and 77: a) a b 2bc) a bd) ae)b)aba 22a a
Page 78 and 79: Ex.24 Express the expressiona) m s
Page 80 and 81: A solution, the solution set, and w
Page 82 and 83: ■ Solve the following equation 3x
Page 84 and 85: sides (subtracting 4 x from both si
Page 86 and 87: Mistake 8.2While solving an equatio
Page 88 and 89: Ex.12 Determine whether the followi
Page 90: Lesson 9___________________________
Page 94 and 95: xy x 1 yFactor x .x( y 1)1yDivide
Page 96 and 97: a) b b) a c) tEx.15. SolveEx.16. So
Page 98 and 99: For each number you should check if
Page 100 and 101: ■ Solve the inequality 4x 9 1.
Page 104 and 105: Ex.10 Graph the following number se
Page 106 and 107: d) z 3e) z 13 Ex.22 Knowing x 1
Page 108 and 109: Example 11.2 The expression( 22 2x
Page 110 and 111: Solution:a) To match the form y mx
Page 112 and 113: a x and b 3 , so now we can rewri
Page 114 and 115: Ex.9 For each of the following expr
Page 116 and 117: 114xc) y 5d) y 3x 2 0e) 3y 6x1f
Page 118 and 119: APPENDIX A:Lesson 1ANSWERS TO EXERC
Page 120 and 121: 49C 3255 2(L+W)62mc75a) a b expon
Page 122 and 123: 3(m n)a(x1)g)h)2tx19s s s sThe opp
Page 124 and 125: 52233x1 2 x5 3 1513 a) m ( 2m) 2mb
Page 126 and 127: c) Numerator: one term, 3ab (with t
Page 128 and 129: 18 a) 9 b) 3 c) 3 d) 3e) 6 f) 279
Page 130 and 131: 11 a) x 1 b)12 a) x abcx a b42 b
Page 132 and 133: c) x 2d) a 7e) x 10f) a 225 a)
Page 134 and 135: x or 4x ( 7) 0; a 4; b 7g) x (
Page 136 and 137: 3. Let m = ─3. Evaluate the follo
Page 138 and 139: 1. Write the following statements a
Page 140 and 141: 6. Solve the following equations:8.
Page 142 and 143: 8. Factor the following expressions
Page 144 and 145: ___________________________________
Page 146: 3 ;b) x 3 y 6 xy 2 A xy 28. a) x
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Math 017 Materials With Exercises

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