Copyright 2012 Pearson Education, Inc. Publishing as Prentice Hall.
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1 Chapter : Equations, Inequalities, and Problem Solving ISM: Intermediate Algebra The solution set is [0, ).. () The solution set is [, ). 0. >.. > >. The solution set is (., ).. The solution set is (, ].. The solution set is [, ) < < 0 < < < > > The solution set is (, ).. ( ) The solution set is (, 0]. 0. ( + ) (+ ) The solution set is, > + + () > + + > ( ) + (+ ) > + + > + > + > > < < The solution set is,. Copyright 0 Pearson Education, Inc. Publishing as Prentice Hall.
2 ISM: Intermediate Algebra Chapter : Equations, Inequalities, and Problem Solving. (+ ) > [ + ( )] > [+ ] > [ ] > 0+ + > 0+ + > > > > The solution set is,.. < + < + < The solution set is (, ).. > < < The solution set is (, ) The solution set is [ 0., ).. The solution set is,.. + < ( + ) + < + < < + < + < > > The solution set is,.. ( + ) + ( + ) ( ) + ( + ) The solution set is [, ).. 0. > > < <. The solution set is (,.). 0. (+ ) + + ( ) The solution set is (, ]. Copyright 0 Pearson Education, Inc. Publishing as Prentice Hall.
3 Chapter : Equations, Inequalities, and Problem Solving ISM: Intermediate Algebra. y (y+ ) ( y ) + 0 y y y y y 0 y + y 0+ y y y y y y y y y The solution set is [, ).. ( + ) < ( ) + ( + ) ( ) < + ( + ) < ( ) () + + < ( ) + + < + + < + + < + < < < < < The solution set is (, ).. 0.( ) <.( ) 0[0.( )] < 0[.( )] ( ) < ( ) < + < + < < < < < The solution set is (, ) The solution set is,. ( ) ( ) ( ) + The solution set is,. > > > ( ) ( ) > + > > + > + > The solution set is (, ). Copyright 0 Pearson Education, Inc. Publishing as Prentice Hall.
4 ISM: Intermediate Algebra Chapter : Equations, Inequalities, and Problem Solving ( + ) The solution set is,.. a. Let be Holden s time on his last trial < < () < < 0. <. The solution is { <.}. b. A time of. minutes or less will result in an average time under.0 minutes.. a. Let be the number of whole ounces mailed ( ) 00[ ( )] 00() 00(0.) + 00[0.( )] 00 + ( ) The solution is { }. b. Seven ounces or less can be mailed for $.00 or less. 0. a. Let be the number of hours parked. So is the number of half-hour intervals parked ( ) 0[ ( )] 0() 0(.0) + 0[0.( )] ( ) The solution is { }. b. With $, you can park for hours or less.. a. Let be the number of daily miles. Then the daily charge for plan B is $( + 0.). Plan A is more economical when the daily charge for Plan B is more than $ > 0. > > 0 The solution is { > 0}. b. Plan A is more economical for more than 0 daily miles.. Stibnite melts at temperatures of F or greater. Use C = ( F ). Replace F with. C = ( F ) C = ( ) C = () C = F = C So stibnite melts at temperatures of C or greater. The solution set is {C C }.. a. Let t be the number of years after.. t+ 0. < c. t + 0. < 0. t < t < 0.. t 0. >.. t >. Copyright 0 Pearson Education, Inc. Publishing as Prentice Hall.
5 Chapter : Equations, Inequalities, and Problem Solving ISM: Intermediate Algebra + = 0 In the year 0 and after cigarette consumption will be less than 0 billion per year. b. answers may vary. Consumption of skim milk is decreasing over time; answers may vary is years after 000, so 0 corresponds to t =. s = 0.t +. s = 0.() +. s =. +. s =. The average consumption of skim milk is epected to be. pounds per person per year in 0.. answers may vary. answers may vary. answers may vary. The integers that are both greater than and less than are {,, }. 0. The integers that are both greater than or equal to and greater than or equal to are {,,,,...}.. = + = + = 0 0 = = The solution set is {}.. + = + = = = = = = The solution set is.. { > }; (, ). (, ] 00. {. < }. 0. To solve >, both sides must be divided by, so the inequality symbol is not reversed. 0. To solve <, both sides must be divided by, so the inequality symbol must be reversed. 0. answers may vary 0. < < < The solution set is (, ). 0. answers may vary. answers may vary. answers may vary Integrated Review. = 0 = The solution set is { }.. < 0 > The solution set is (, ).. The solution set is, The solution set is [, ). Copyright 0 Pearson Education, Inc. Publishing as Prentice Hall.
6 ISM: Intermediate Algebra Chapter : Equations, Inequalities, and Problem Solving. ( y ) = ( y ) y = y y = y y = 0 y = 0 The solution set is {0}... 0 The solution set is,. 0 The solution set is,.. ( y+ ) = ( y+ ) y+ 0= y+ 0 y = y y = 0 The solution set is {0}.. < ( ) < 0< False; the solution set is The solution set is,.. +. =. = = =. The solution set is {.}.. + = = 0 = The solution set is {}.. + = + + = = = = The solution set is { }.. + < < < The solution set is (, ).. = 0 0 = 0 0 = 0( ) = 0 0 = 0 0 = 0 0 = 0 The solution set is.. = ( ) = = + = = The solution set is {}.. ( ) > 0 > 0 > > The solution set is (, )... =. =. =. The solution set is {.}. Copyright 0 Pearson Education, Inc. Publishing as Prentice Hall.
7 Chapter : Equations, Inequalities, and Problem Solving ISM: Intermediate Algebra. ( b ) (b ) = b+ b+ b+ = b+ b+ = b+ b = b 0b = b = = 0 The solution set is. 0. ( + ) < ( + ) + + < < + < True The solution set is (, ). t+ + t. = + t+ + t = + + t (t + ) = + () t+ = ( + t) + t+ = 0 + t+ t+ = t+ t = t+ t = t = The solution set is {}.. ( ) = ( ) = = = True The solution set is { is a real number} < < < 0 ( + ) + ( ) < < 0 < 0 < < The solution set is (, ).. y y y+ + = 0 y y y = 0 y y = ( y + ) 0y+ y = y+ y = y+ y = y = The solution set is.. ( ) + > ( ) 0+ > 0> > + > The solution set is (, ).. ( ) ( ) The solution set is (, ].. (+ ) ( ) + (+ ) ( ) + (+ ) ( ) ( ) () + (+ ) ( ) The solution set is,. Copyright 0 Pearson Education, Inc. Publishing as Prentice Hall.
8 ISM: Intermediate Algebra Chapter : Equations, Inequalities, and Problem Solving. ( 0) > (+ ) ( 0) ( ) > + ( 0) ( ) ( ) () > + ( 0) > (+ ) 0 > 0+ 0 > 0 > 0+ > < The solution set is,. Section. Practice. The numbers,, and are in both sets. The intersection is {,, }.. + < and < < and < < and < The solution set is (, ) (, ) = (, ).. 0 and + 0 and 0 and There is no number greater than or equal to 0 and less than or equal to. The solution set is.. < < < < < < > > The solution set is (, ).. < + < + < ( ) < () < < < The solution set is,.. The numbers that are in either set are {,,,,, }. This set is the union.. 0 or or or The solution set is (, ] [, ).. or or or The solution set is (, ). Vocabulary and Readiness Check. Two inequalities joined by the words and or or are called compound inequalities.. The word and means intersection.. The word or means union.. The symbol means intersection.. The symbol represents union.. The symbol is the empty set.. The inequality < means and <.. { < 0 and > 0} =. Eercise Set.. C D = {,,, } {,,, } = {, } Copyright 0 Pearson Education, Inc. Publishing as Prentice Hall.
9 Chapter : Equations, Inequalities, and Problem Solving ISM: Intermediate Algebra. A D = { is an even integer} {,,, } = { is an even integer or = or = }. A B= { is an even integer} { is an odd integer} =. B D = { is an odd integer} {,,, } = { is an odd integer or = or = } 0. B C = { is an odd integer} {,,, } = {, }. A C = { is an even integer} {,,, } = { is an even integer or = or = }.. The solution set is [, 0].. The solution set is. The solution set is (, ) and and 0 and The solution set is [, ).. + > 0 and > 0 > and > 0 > and > 0 The solution set is (0, ). 0 Copyright 0 Pearson Education, Inc. Publishing as Prentice Hall.
10 ISM: Intermediate Algebra Chapter : Equations, Inequalities, and Problem Solving. and 0 and The solution set is [, ] The solution set is [, ].. < + < < + < < < < < < < The solution set is,. 0.. < < + < + < + < < () < < () < < The solution set is (, ). + + ( ) () + + The solution set is,... The solution set is (, ] [, ). The solution set is (, ) or or or The solution set is [, ).. + < 0 or > < or > The solution set is (, ) (, ).. ( ) or or 0 or 0 or The solution set is [, )... < and < The solution set is, (,) =,. < or < The solution set is, or (, ) = (, ).. The solution set is (, ). Copyright 0 Pearson Education, Inc. Publishing as Prentice Hall.
11 Chapter : Equations, Inequalities, and Problem Solving ISM: Intermediate Algebra 0. < + < < + < < < 0 0 < < < < The solution set is,.. < + < < + < () < ( ) + < < + < < + < < < < < < < The solution set is,.. and > and < and < The solution set is [, ) (, ) = or < or > ( ) or > or > The solution set is, (, ).. < < ( ) < < () < < + < + < + < < > > > > The solution set is,. 0. < ( + ) < + < + < 0 0 < < 0 The solution set is,0.. 0 and + < 0 and < 0 and > The solution set is (, 0] (, ) = (, 0].. < or + < 0 > or < > or < The solution set is (, ) (, ).. < or > > or > > or < The solution set is (, ) (, ). Copyright 0 Pearson Education, Inc. Publishing as Prentice Hall.
12 ISM: Intermediate Algebra Chapter : Equations, Inequalities, and Problem Solving. 0. < < 0 0 < + + < + < < < The solution set is,. < < < < < < < < < < > > > > < < The solution set is (, ).. 0. < < 0. 0( 0.) < 0( ) < 0(0.) < 0(0. ) + 0(0.) < < + < < + < < < < <. < < 0. The solution set is (., 0.).. = =. ( ) + 0 = = + 0 =. = when = or =. The solution set is {, }. 0. There are no values of such that =, so the solution set is.. From the graph, we see that the number of single-family housing starts that are less than 000 or the number of single-family housing completions greater than 00 are for the years 00, 00, 00, 00, and 00.. answers may vary. < + < < + and + < < + and < < and < > and > The solution set is (, ) (, ) = (, ).. ( ) 0 ( ) and 0 + and and and and The solution set is [, ) (, ] = [, ] C 0 ( F ) ( 0) ( ) () F F. + F +. + F. The temperatures ranged from F to. F.. Let be her final eam score (0) () To earn a B in the course, her final eam grade must be between. and 00 (assuming she can t earn etra credit.) Section. Practice. q = q = or q = The solution set is {, }. Copyright 0 Pearson Education, Inc. Publishing as Prentice Hall.
13 Chapter : Equations, Inequalities, and Problem Solving ISM: Intermediate Algebra. = = or = = or = = or = The solution set is {, }.. + = + = or + = = or = = 0 or = 0 The solutions are 0 and = = = or = = or = The solutions are and.. z = 0 The solution is 0.. z + = z = z = The absolute value of a number is never negative, so there is no solution. The solution set is { } or.. + = The absolute value of a number is never negative, so there is no solution. The solution set is { } or.. + = + = or + = ( ) + = + = + = + = = = = The solutions are and.. = = = = 0 = or = ( ) = + = False The solution is. Vocabulary and Readiness Check. = C. = or =. = 0 A. = 0. = + B. = + or = ( + ). + = E. + = or + =. + = D. Eercise Set.. y = y = or y =. n =. n =. or n =. n =. or n =.. + n = + n = or + n = n = 0 or n = n = or n = n. + = n n + = or + = n n = or = n = or n = 0. + = = = or = Copyright 0 Pearson Education, Inc. Publishing as Prentice Hall.
14 ISM: Intermediate Algebra Chapter : Equations, Inequalities, and Problem Solving. = = 0 = 0 or = 0 = or =. z = 0 z = 0 z = 0. z + = z = which is impossible. The solution set is.. y + = 0 y + = 0 y = y = 0. y + = y + y+ = (y+ ) or y+ = y+ y+ = y or y = y = or y = y = or y =. = + = (+ ) or = + = or = = 0 or false = 0 The only solution is 0.. = = or =. y = y = or y =. The absolute value of any epression is never negative, so no solution eists. The solution set is. 0. m + = m+ = or m+ = m = 0 or m = 0 m = 0 or 0 m = m = 0 or m =. z + = z = z = or z = z = or z =. The absolute value of any epression is never negative, so no solution eists. The solution set is.. + = + = + = or + = = or =. The absolute value of any epression is never negative, so no solution eists. The solution set is. 0. The absolute value of any epression is never negative, so no solution eists. The solution set is.. = 0 = 0 = =. + m = + m = + m = or + m = m = 0 or m = m = 0 or m = Copyright 0 Pearson Education, Inc. Publishing as Prentice Hall.
15 Chapter : Equations, Inequalities, and Problem Solving ISM: Intermediate Algebra. c = c = or c = c = or c = c = or c = c = or c =. + = + = + = or + = = or = = or = 0. + n = n + + n = n+ or + n = (n+ ) n = or + n = n n = or 0n = n = or n =. y = y = The absolute value of any epression is never negative, so no solution eists. The solution set is.. n + = n + n+ = (n+ ) or n+ = n+ n+ = n or = n = or false n =. The only solution is. + n = + n + n = or = + n= or + n = n= or n = n= or n =. + m = m = m = or m = m = or m = = = + + = or = + = or + = = 0 or = = or =. z = z z = ( z) or z = z z = + z or z = z = or z = z =. r r = = r r = or = r = 0 or r = 0 r = or r = r = or r =. y = y + y = ( y+ ) or y = y+ y = y or = y = or = y false or = y The only solution is.. d + = d + = The absolute value of any epression is never negative, so no solution eists. The solution set is. 0. From the circle graph, mozzarella cheese had the highest US production in 00. Copyright 0 Pearson Education, Inc. Publishing as Prentice Hall.
16 ISM: Intermediate Algebra Chapter : Equations, Inequalities, and Problem Solving. In 00, cream cheese accounted for % of the total cheese production. % of,,000,000 is 0.0(,,000,000) =,00,000,00,000 pounds of cream cheese was produced in the US in 00.. answers may vary. y < 0 has no solutions.. Since absolute value is never negative, the solution set is. 0. All numbers whose distance from 0 is units is written as =.. answers may vary. =. answers may vary. = 0. a + b = c a. one solution if c = 0 b. no solutions if c is a negative number c. two solutions if c is a positive number Section. Practice. < The solution set of this inequality contains all numbers whose distance from 0 is less than. The solution set is (, ).. b + < < b + < < b + < < b < (, ) , + < The absolute value of a number is always nonnegative and can never be less than. The solution set is { } or. ( ) 0 ( ) = 0 ( ) = (0) ( ) = 0 = 0 = = The solution set is {}.. y + y+ or y+ y+ or y+ y 0 or y (, 0] [, ). + + > + + > + > The absolute value of any number is always nonnegative and thus is always greater than. (, ) Copyright 0 Pearson Education, Inc. Publishing as Prentice Hall.
17 Chapter : Equations, Inequalities, and Problem Solving ISM: Intermediate Algebra. > + > + > < or > < ( ) or > () < or > < 0 or > (, 0) (, ) Vocabulary and Readiness Check. D. E. C. B. A The solution set is 0. +,. The solution set is [, ].. < The absolute value of an epression is never negative, so no solution eists. The solution set is.. z + < z + < < z + < < z + < < z < The solution set is (, ). Eercise Set.. < < < The solution set is (, ).. y y or y The solution set is (, ] [, ).. y y y The solution set is [, ].. or or The solution set is (, ] [, ).. + < < + < 0 < < The solution set is ( 0, ).. 0. > > < or > The solution set is (, ) (, ).. > An absolute value is always greater than a negative number. Thus, the answer is (, ). Copyright 0 Pearson Education, Inc. Publishing as Prentice Hall.
18 ISM: Intermediate Algebra Chapter : Equations, Inequalities, and Problem Solving > 0 + > 0 + < or 0 + > < or > < or > The solution set is, (, )., [, ). + < < An absolute value is never negative, so no solution eists. The solution set is.. 0 An absolute value is always greater than or equal to 0. Thus, the answer is (, ). 0. An absolute value is never negative, so no solution eists. The solution set is.. < 0 The absolute value of an epression is never negative, so no solution eists. The solution set is. 0. z < < z < (, ). + < < + < 0 < < < < The solution set is, or 0 (, 0] [0, ) [, ] or or or or. + > + + > + + > + < or + > < or > (, ) (, ). < 0 An absolute value is never negative, so no solution eists. The solution set is.. + An absolute value is always greater than or equal to 0. Thus, the answer is (, ). Copyright 0 Pearson Education, Inc. Publishing as Prentice Hall.
19 Chapter : Equations, Inequalities, and Problem Solving ISM: Intermediate Algebra 0. + The solution set is,.. 0,. or or or, [, ). + An absolute value is always greater than or equal to 0. Thus, the answer is (, ) = 0 + = 0 = = or + or + or The solution set is (, ] [, ) < < + + < < + < < < < < < <, 0 Copyright 0 Pearson Education, Inc. Publishing as Prentice Hall.
20 ISM: Intermediate Algebra Chapter : Equations, Inequalities, and Problem Solving. + < + < < + < < + 0 < < 0 < 0 < < < < 0, 0. > < or > < or > 0 < or > (, ) (, ). = = or = = or = = or = The solution set is, or + 0 or The solution set is (, ] [, ) An absolute value is always greater than or equal to 0. Thus, the answer is (, ).. + or 0 or 0 or The solution set is (, 0],.. + = = = or = = or = = or = The solution set is,.. = An absolute value is never negative, so no solution eists. The solution set is = = or = = 0 or = 0 = or = The solution set is {, }. < < < 0 < < 0 < < < < The solution set is,. P (rolling a ) =. P (rolling a 0) = 0. P(rolling a,,,,, or ) = 0. y = ( ) = + = = = Copyright 0 Pearson Education, Inc. Publishing as Prentice Hall.
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