Math 017 Materials With Exercises

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$Math 171 Review for the Final Exam$

$Math 171 Test 2$

$MATH 171 SYLLABUS$

2 x 2 xFor example, and thus also2 x 2 x (notice, that we switched the left side with7 7 77 7 7the right one of the equation, so both equations are true, just like if 2 3 5 then 5 2 3 ). It isalso true thata 3 a 3 2 y 2 y and .x x x x 3 x 3 x 3The rules for multiplication and division of fractions:Rule for Multiplicationand Division ofFractionsa xyaxya xy1x y x yxy, y 0Thus, we should recognize that the following are true:x 1x2 2, 3x3 5 5x1 a b, and ( a b)3 31Finally, you might recall that 2would like to see how to do it) that121 2. Similarly, one may show (ask your instructor, if youRule for Negative Signs inFractionsx x x , y 0y y yExample 3.7 Rewrite each of the following expressions as a sum or a difference of two expressions.a b a b a b a bUse or (we assume that c 0 ) . Indicate with thec c c c c cequal sign that the resulting expressions are equivalent.2 sa)52a 2b)5 xSolution:a)b)2 s 2 s5 5 522a 2 a 2 5 x 5 x 5 x28
ax aExample 3.8 Use the fact that x to rewrite the following expressions as a product of ay ynumerical factor and an algebraic expression.2bx ba) b)5 5Solution:2b2 2a) b ; is a numerical factor.5 5 5x b 1b) ( x b)Notice the use of parentheses. The entire expression in the5 51numerator should be multiplied by . Had we omitted the parentheses, only x would51have been multiplied by . 5Example 3.9 Rewrite each of the following expressions in their equivalent form as a single fraction.6xa) ab) 211yc) 1 ( a 2 1)3a 2bd) x 2 x 2a 1 2a 1 b ce) af) 2 4s4sx xSolution:6 6aa) a 11 11x 2xb) 2 y y221 2 1( a 1)a 1c) ( a 1) Write a 2 1instead of 1(a 2 1)!33 3a 2ba 2bd) x 2 x 2 x 222a 1 2 a a a aa ae) a First replace by , and4s4s4s4s4s4s4s21 a2 aby (equals can be substituted by equals). Then subtract, just as you subtract4s4sfractions.a 1b c 2( a 1)b c 2( a 1) ( b c)f) 2 Notice the use ofx x x x xparentheses.29
Page 1 and 2: Math 017MaterialsWithExercises
Page 3 and 4: TABLE OF CONTENTSLesson 1Variables
Page 5 and 6: Lesson 1___________________________
Page 7 and 8: e) „minus x ‟ or „the opposit
Page 9 and 10: For example,Evaluate 5 x when x 10
Page 11 and 12: 3xd) x( y)e) 2f) 2x yz w(t)Ex.4 T
Page 13 and 14: Ex.16 Let x 3. Rewrite the express
Page 15 and 16: e) x5f) x2Ex.28 Substitute“undefi
Page 17 and 18: Lesson 2___________________________
Page 19: Solution:Please, notice the use of
Page 22 and 23: g)i)4( a 2)h)8y (x)4(ab)j) ( a d)
Page 24 and 25: 1 2Ex.19 If possible, evaluate when
Page 26 and 27: Lesson 3___________________________
Page 28 and 29: Commutative Propertyof Additionx y
Page 32 and 33: Example 3.10 Determine which of the
Page 34 and 35: Exercises with Answers (For answers
Page 36 and 37: Ex.16 Write the following expressio
Page 38 and 39: s) ( 0.2xy)( 0.3z)t)4x1Ex.24 Is 1
Page 40 and 41: Lesson 4___________________________
Page 42 and 43: 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 94 and 95:
xy x 1 yFactor x .x( y 1)1yDivide
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a) b b) a c) tEx.15. SolveEx.16. So
Page 98 and 99:
For each number you should check if
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■ 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
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d) z 3e) z 13 Ex.22 Knowing x 1
Page 108 and 109:
Example 11.2 The expression( 22 2x
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Solution:a) To match the form y mx
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a x and b 3 , so now we can rewri
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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
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49C 3255 2(L+W)62mc75a) a b expon
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3(m n)a(x1)g)h)2tx19s s s sThe opp
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52233x1 2 x5 3 1513 a) m ( 2m) 2mb
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c) Numerator: one term, 3ab (with t
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18 a) 9 b) 3 c) 3 d) 3e) 6 f) 279
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11 a) x 1 b)12 a) x abcx a b42 b
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c) x 2d) a 7e) x 10f) a 225 a)
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x or 4x ( 7) 0; a 4; b 7g) x (
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3. Let m = ─3. Evaluate the follo
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1. Write the following statements a
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6. Solve the following equations:8.
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8. Factor the following expressions
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___________________________________
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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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