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 inequality 4x 9 1. 4x 9 1Subtract 9 from both sides. 4x 9 9 19Perform the indicated operations (on each sideseparately). 4x 8Divide both sides by 4 and reverse thedirection of the inequality sign. 4x 8Cancel fractions. 4 4x 2The solution of the inequality 4x 9 1is x 2■This means that all numbers that are less than or equal to 2 make this inequality true. That is, if in theoriginal inequality x is replaced by any number less than or equal to 2, the resulting numericalstatement will always be true. It also means that any other number, i.e. any number that is greater than2, when substituted for x , would give us a false numerical statement.Observe that there are infinitely many solutions and that is why, instead of listing them, we must usethe appropriate inequality symbol in recording the result.Example 10.5 Solve the following inequalities and graph their solution.a) x 4b) 3x 7 2Solution:a) x 4Multiply both sides by 1, remember about reversing theinequality sign.( 1)(x ) ( 1)(4)Perform the indicated operations.x 4The graph of the solution:b) 3x 7 2Add 7 to both sides.3x 7 7 2 7 Simplify.3x 5Divide each side by 3.3x5 3 3Simplify.5x 3The graph of the solution:98
4 x x 2Example 10.6 Solve the following inequality 52 4Solution:4 x x 2To get rid of fractions, multiply both sides by 4 ( a 52 4common multiple of both denominators). 4 x x 2 4 54 Apply the Distributive Law to remove parentheses. 2 4 4 x x 24 4 54 Simplify (place the parentheses correctly)2 42(4 x ) ( x 2) 20 Again apply the Distributive Law to removeparentheses.8 2x x 2 20Collect like terms on each side of the inequalityseparately 3x 6 20Subtract 6 from both sides. 3x 6 6 20 6Simplify. 3x 14Divide each side by 3 and reverse the inequalitysign. 3x14Simplify. 3 314x 34 x x 214The solution of 5 is x .2 43Linear inequalities with no solution or solution consisting of all real numbersIt might happen that during the process of solving an inequality, the variable gets cancelled and theinequality reduces to a numerical statement (you can remember this occurring when solving someequations).■ Solve the following inequality x 3 x 5.x 3 x 5Subtract x from each sidex 3 x x 5 xSimplify3 5The statement 3 5 is always true, regardless of the value of x . Thus, the solution set of x 3 x 5consists of all real numbers. ■99
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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
Page 50 and 51: 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 102 and 103: ■ Solve the following inequality
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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