Math 017 Materials With Exercises

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$Math 171 Review for the Final Exam$

$Math 171 Test 2$

$MATH 171 SYLLABUS$

xy x 1 yFactor x .x( y 1)1yDivide each side by y 11yFactor 1 from the numerator (or you couldx y 1choose to factor 1 from the denominator).1(y 1)x Cancel y 1.y 1x 1<strong>Exercises</strong> with Answers (For answers see Appendix A)When needed, assume that all denominators (divisors) are not equal to zero.Ex.1 Solve the following equations.x 2xa) 5b) 1 8x 42xx c) 3x 1 0d)1 1x53 21 1 3x 2 3e) y yf) 5 5 102 3 4Ex.2 Solve the following equations.a) 8x 2 3x 5( x 2)b) x ( 2 x) 5x12x2 53x3c) 1 a d) 13 62 4e) 4(3x 1)12x 2f) 4x 2 3x (1 5x)g) 2( x 3) 4 x 2h)x 3 1x2 5i) 3 (4 x) 2(x 6) x5 7 3j) x x 8 12 4k) 3(4 7x)15(3 x)l) ( x 2) 2( x 1) 3x 5Ex.3 Let A 2x,B x.Find x , so the following are true (Hint: Substitute algebraicexpressions for A and B . Then solve for x ).a) A B 0b) A 3B1A Bc) 3 8Ex.4 Let P 3(x 1)and Q 4x 5. Find x such that the following is true (Hint: Substitutealgebraic expressions for P and Q . Then solve for x ).a) P Qb) P Q92
Qc) P2Ex.5 Let x 3 a 2, y 2a1,z 2 a . Find a , so the following are true (Hint: Substitutealgebraic expressions for x, y,and z . Then solve for a ).a) x y zb) 2 x y zx y zc) 8 2 4x 1Ex.6 Does the following statement make sense: “Solve 5y2xEx.7 Solve for x . a) 72 xb) bafor x“? Why or why not?Ex.8 Solve for x . a) x 3 8b) x a bEx.9 Solve for x . a) 3x 7 11b) ax b cEx.10 Solve for x . a) 5x 2x 6 0 b) ax bx c 0Ex.11 Solve for x . a) 4x 2( x 1)b) ax b( x c)Ex.12. Solve for the indicated variable. Simplify your answer whenever possible.ba) x a for x b) ac for baa bc) for a d) ax b 4bfor a3b c2ae) 2 3a for u f) abc (ac) for bu2mg) 4 n for m h) 2x y t 3xfor y2n33i) x xy 2x for y j) AX A 1 X for A2k) s( x 1) s for x l) ax by 3ax 4byfor am) 3 ( v t) s for v n) ax x( a 2) 1for xm 2no) 2n m for xxp) mb 2mb 3bfor mEx.13 Solve the following equationx d e forya) d b) x c) yEx.14 Solve the following equation3 at b 2at t for93
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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
Page 34 and 35:
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
Page 44 and 45: For your convenience, we will displ
Page 46 and 47: 9 818081a) 9 98097 6 76134 4 4 4
Page 48 and 49: 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 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 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
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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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