Elementary & Intermediate Algebra
Elementary & Intermediate Algebra
3rd Edition
ISBN: 9780321880116
Author: Michael Sullivan III, Katherine R. Struve, Janet Mazzarella
Publisher: PEARSON
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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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Chapter 2, Problem 1PCT

Determine whether the given value of the variable is a solution of the equation. Answer Yes or No.

4 − (6 − x) = 5x – 8

a. x = 3 2

b. x = − 5 2

a.

Expert Solution
Check Mark
To determine

Whether x=32 is a solution of the linear equation 4−(6−x)=5x−8 or not.

Answer to Problem 1PCT

Yes, x=32 is a solution of the linear equation 4−(6−x)=5x−8.

Explanation of Solution

Definition used:

Solution of a linear equation:

The value(s) of the variable that satisfies the equation or makes the equation a true statement is known as solution(s) of a linear equation.

Calculation:

Consider the linear equation 4−(6−x)=5x−8.

Replace the variable x with 32.

4−(6−(32))=5(32)−8

Simplify the values.

4−(6−(32))=?5(32)−84−(6⋅22−32)=?152−84−(12−32)=?152−8⋅224−(92)=?15−162

Simplify further as follows.

4⋅22−92=?−128−92=?−12−12=−12         [TRUE]

Here, both sides of the equation are equal when the variable x is replaced by 32.

Therefore, x=32 is a solution of the linear equation 4−(6−x)=5x−8.

b.

Expert Solution
Check Mark
To determine

Whether x=−52 is a solution of the linear equation 4−(6−x)=5x−8 or not.

Answer to Problem 1PCT

No, x=−52 is not a solution of the linear equation 4−(6−x)=5x−8.

Explanation of Solution

Consider the linear equation 4−(6−x)=5x−8.

Replace the variable x with −52.

4−(6−(−52))=5(−52)−8

Simplify the values.

4−(6−(−52))=?5(−52)−84−(6⋅22+52)=?−252−84−(12+52)=?−252−8⋅224−(172)=?−25−162

Simplify further as follows.

4⋅22−172=?−4128−172=?−412−92≠−412         [FALSE]

Here, both sides of the equation are not equal when the variable x is replaced by −52.

Therefore, x=−52 is not a solution of the linear equation 4−(6−x)=5x−8.

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Chapter 2 Solutions

Elementary & Intermediate Algebra

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Bridges The longest suspension bridge in the...Ch. 2.5 - Prob. 68ECh. 2.5 - Buying a Motorcycle The total price for a new...Ch. 2.5 - Prob. 70ECh. 2.5 - Prob. 71ECh. 2.5 - Finance A total of 10,000 is to be divided between...Ch. 2.5 - Prob. 73ECh. 2.5 - Investments Jack and Diane have 40,000 to invest....Ch. 2.5 - Prob. 75ECh. 2.5 - Books A paperback edition of a book costs 12.50...Ch. 2.5 - Income On a joint income tax return, Elizabeth...Ch. 2.5 - Prob. 78ECh. 2.5 - Prob. 79ECh. 2.5 - Cellular Telephones You need a new cell phone for...Ch. 2.5 - Prob. 81ECh. 2.5 - Comparing Job Offers Hans has just been offered...Ch. 2.5 - Prob. 83ECh. 2.5 - Camping Trip Jaime Juarez purchased some new...Ch. 2.5 - Prob. 85ECh. 2.5 - Computing Grades Going into the final exam, which...Ch. 2.5 - In Problems 9194, write a problem that would...Ch. 2.5 - Prob. 88ECh. 2.5 - Prob. 89ECh. 2.5 - Prob. 90ECh. 2.5 - Prob. 91ECh. 2.5 - Angles The sum of the measures of the three angles...Ch. 2.5 - Prob. 93ECh. 2.5 - Prob. 94ECh. 2.5 - Prob. 95ECh. 2.5 - Using the algebraic expression 3x + 5, make up a...Ch. 2.6 - Percent means divided by ___________.Ch. 2.6 - True or False 40% of 120 means 0.4 120.Ch. 2.6 - Prob. 3ECh. 2.6 - Prob. 4ECh. 2.6 - Prob. 5ECh. 2.6 - Prob. 6ECh. 2.6 - Prob. 7ECh. 2.6 - Prob. 8ECh. 2.6 - Prob. 9ECh. 2.6 - Prob. 10ECh. 2.6 - 14.8 is 18.5% of what number?Ch. 2.6 - Prob. 12ECh. 2.6 - Prob. 13ECh. 2.6 - Prob. 14ECh. 2.6 - Prob. 15ECh. 2.6 - Prob. 16ECh. 2.6 - Prob. 17ECh. 2.6 - Prob. 18ECh. 2.6 - Prob. 19ECh. 2.6 - In Problems 1936, find the unknown in each percent...Ch. 2.6 - In Problems 1936, find the unknown in each percent...Ch. 2.6 - In Problems 1936, find the unknown in each percent...Ch. 2.6 - Prob. 23ECh. 2.6 - In Problems 1936, find the unknown in each percent...Ch. 2.6 - In Problems 1936, find the unknown in each percent...Ch. 2.6 - In Problems 1936, find the unknown in each percent...Ch. 2.6 - Prob. 27ECh. 2.6 - In Problems 1936, find the unknown in each percent...Ch. 2.6 - Prob. 29ECh. 2.6 - In Problems 1936, find the unknown in each percent...Ch. 2.6 - In Problems 1936, find the unknown in each percent...Ch. 2.6 - In Problems 1936, find the unknown in each percent...Ch. 2.6 - Prob. 33ECh. 2.6 - In Problems 1936, find the unknown in each percent...Ch. 2.6 - Prob. 35ECh. 2.6 - In Problems 1936, find the unknown in each percent...Ch. 2.6 - Prob. 37ECh. 2.6 - Prob. 38ECh. 2.6 - Prob. 39ECh. 2.6 - Bad Investment After Mrs. Fisher lost 9% of her...Ch. 2.6 - Pay Raise MaryBeth works from home as a graphic...Ch. 2.6 - Good Investment Perry just learned that his house...Ch. 2.6 - Prob. 43ECh. 2.6 - Hailstorm Toyota Town had a 15%-off sale on...Ch. 2.6 - Prob. 45ECh. 2.6 - Discount Pricing A wool suit that was originally...Ch. 2.6 - Prob. 47ECh. 2.6 - Prob. 48ECh. 2.6 - Prob. 49ECh. 2.6 - Voting On a committee consisting of Republicans...Ch. 2.6 - Commission Melanie receives a 3% commission on...Ch. 2.6 - Prob. 52ECh. 2.6 - Prob. 53ECh. 2.6 - Grades If 15% of Grants astronomy class received...Ch. 2.6 - Prob. 55ECh. 2.6 - Prob. 56ECh. 2.6 - Prob. 57ECh. 2.6 - Prob. 58ECh. 2.6 - Prob. 59ECh. 2.6 - In Problems 6065, find the percent increase or...Ch. 2.6 - In Problems 6065, find the percent increase or...Ch. 2.6 - Prob. 62ECh. 2.6 - Prob. 63ECh. 2.6 - Prob. 64ECh. 2.6 - Prob. 65ECh. 2.6 - Prob. 66ECh. 2.6 - Prob. 67ECh. 2.6 - An item is reduced by 10% and then this is reduced...Ch. 2.7 - Complementary angles are angles whose measures...Ch. 2.7 - Prob. 2ECh. 2.7 - Prob. 3ECh. 2.7 - Prob. 4ECh. 2.7 - Prob. 5ECh. 2.7 - Prob. 6ECh. 2.7 - Prob. 7ECh. 2.7 - Prob. 8ECh. 2.7 - Prob. 9ECh. 2.7 - True or False When using d = rt to calculate the...Ch. 2.7 - Prob. 11ECh. 2.7 - Tanya, a long-distance runner, runs at an average...Ch. 2.7 - Prob. 13ECh. 2.7 - In Problems 1316, identify the measure of each of...Ch. 2.7 - Prob. 15ECh. 2.7 - In Problems 1316, identify the measure of each of...Ch. 2.7 - Prob. 17ECh. 2.7 - In Problems 1720, find the measures of the angles...Ch. 2.7 - Prob. 19ECh. 2.7 - Prob. 20ECh. 2.7 - In Problems 2126, use a formula from geometry to...Ch. 2.7 - In Problems 2126, use a formula from geometry to...Ch. 2.7 - In Problems 2126, use a formula from geometry to...Ch. 2.7 - Prob. 24ECh. 2.7 - Prob. 25ECh. 2.7 - Prob. 26ECh. 2.7 - Prob. 27ECh. 2.7 - In Problems 27 and 28, set up the model to solve...Ch. 2.7 - Prob. 29ECh. 2.7 - Prob. 30ECh. 2.7 - Isosceles Triangle An isosceles triangle has...Ch. 2.7 - Prob. 32ECh. 2.7 - Billboard A billboard along a highway has a...Ch. 2.7 - Buying Wallpaper Erika is buying wallpaper for her...Ch. 2.7 - Prob. 35ECh. 2.7 - Prob. 36ECh. 2.7 - Prob. 37ECh. 2.7 - Table The Jacksons are having a custom rectangular...Ch. 2.7 - Prob. 39ECh. 2.7 - Cyclists Two cyclists leave a city at the same...Ch. 2.7 - Road Trip Two cars leave a city on the same road,...Ch. 2.7 - Passenger and Freight Trains Two trains leave a...Ch. 2.7 - Prob. 43ECh. 2.7 - Prob. 44ECh. 2.7 - Prob. 45ECh. 2.7 - Prob. 46ECh. 2.7 - Prob. 47ECh. 2.7 - Prob. 48ECh. 2.7 - Prob. 49ECh. 2.7 - In Problems 4954, given L1||L2, use the...Ch. 2.7 - In Problems 4954, given L1||L2, use the...Ch. 2.7 - Prob. 52ECh. 2.7 - Prob. 53ECh. 2.7 - In Problems 4954, given L1||L2, use the...Ch. 2.7 - Prob. 55ECh. 2.7 - Prob. 56ECh. 2.7 - When setting up a uniform motion problem, you...Ch. 2.8 - True or False To graph an inequality that contains...Ch. 2.8 - Prob. 2ECh. 2.8 - Prob. 3ECh. 2.8 - Prob. 4ECh. 2.8 - Prob. 5ECh. 2.8 - Prob. 6ECh. 2.8 - True or False The inequality x 4 is written in...Ch. 2.8 - Prob. 8ECh. 2.8 - Prob. 9ECh. 2.8 - Prob. 10ECh. 2.8 - In Problems 811, write the inequality in interval...Ch. 2.8 - Prob. 12ECh. 2.8 - Prob. 13ECh. 2.8 - Prob. 14ECh. 2.8 - Prob. 15ECh. 2.8 - Prob. 16ECh. 2.8 - Prob. 17ECh. 2.8 - Prob. 18ECh. 2.8 - Prob. 19ECh. 2.8 - Prob. 20ECh. 2.8 - In Problems 2023, find the solution of the linear...Ch. 2.8 - Prob. 22ECh. 2.8 - Prob. 23ECh. 2.8 - Prob. 24ECh. 2.8 - Prob. 25ECh. 2.8 - Prob. 26ECh. 2.8 - Prob. 27ECh. 2.8 - Prob. 28ECh. 2.8 - In Problems 28 and 29, find the solution of the...Ch. 2.8 - Prob. 30ECh. 2.8 - True or False When you are solving an inequality,...Ch. 2.8 - In Problems 3235, find the solution of the...Ch. 2.8 - Prob. 33ECh. 2.8 - Prob. 34ECh. 2.8 - Prob. 35ECh. 2.8 - Prob. 36ECh. 2.8 - Prob. 37ECh. 2.8 - In Problems 3744, graph each inequality on a...Ch. 2.8 - Prob. 39ECh. 2.8 - In Problems 3744, graph each inequality on a...Ch. 2.8 - In Problems 3744, graph each inequality on a...Ch. 2.8 - In Problems 3744, graph each inequality on a...Ch. 2.8 - Prob. 43ECh. 2.8 - In Problems 3744, graph each inequality on a...Ch. 2.8 - Prob. 45ECh. 2.8 - In Problems 4550, use interval notation to express...Ch. 2.8 - Prob. 47ECh. 2.8 - In Problems 4550, use interval notation to express...Ch. 2.8 - Prob. 49ECh. 2.8 - In Problems 4550, use interval notation to express...Ch. 2.8 - Prob. 51ECh. 2.8 - Prob. 52ECh. 2.8 - Prob. 53ECh. 2.8 - Prob. 54ECh. 2.8 - Prob. 55ECh. 2.8 - Prob. 56ECh. 2.8 - Prob. 57ECh. 2.8 - Prob. 58ECh. 2.8 - Prob. 59ECh. 2.8 - In Problems 5988, solve the inequality. Express...Ch. 2.8 - Prob. 61ECh. 2.8 - In Problems 5988, solve the inequality. Express...Ch. 2.8 - Prob. 63ECh. 2.8 - In Problems 5988, solve the inequality. Express...Ch. 2.8 - Prob. 65ECh. 2.8 - In Problems 5988, solve the inequality. Express...Ch. 2.8 - Prob. 67ECh. 2.8 - In Problems 5988, solve the inequality. Express...Ch. 2.8 - Prob. 69ECh. 2.8 - In Problems 5988, solve the inequality. Express...Ch. 2.8 - Prob. 71ECh. 2.8 - In Problems 5988, solve the inequality. Express...Ch. 2.8 - Prob. 73ECh. 2.8 - In Problems 5988, solve the inequality. Express...Ch. 2.8 - Prob. 75ECh. 2.8 - In Problems 5988, solve the inequality. Express...Ch. 2.8 - Prob. 77ECh. 2.8 - Prob. 78ECh. 2.8 - Prob. 79ECh. 2.8 - In Problems 5988, solve the inequality. Express...Ch. 2.8 - Prob. 81ECh. 2.8 - In Problems 5988, solve the inequality. Express...Ch. 2.8 - Prob. 83ECh. 2.8 - Prob. 84ECh. 2.8 - Prob. 85ECh. 2.8 - In Problems 5988, solve the inequality. Express...Ch. 2.8 - Prob. 87ECh. 2.8 - In Problems 5988, solve the inequality. Express...Ch. 2.8 - Prob. 89ECh. 2.8 - In Problems 8998, write the given statement using...Ch. 2.8 - Prob. 91ECh. 2.8 - Prob. 92ECh. 2.8 - Prob. 93ECh. 2.8 - In Problems 8998, write the given statement using...Ch. 2.8 - Prob. 95ECh. 2.8 - In Problems 8998, write the given statement using...Ch. 2.8 - Prob. 97ECh. 2.8 - Prob. 98ECh. 2.8 - Prob. 99ECh. 2.8 - In Problems 99116, solve the inequality and...Ch. 2.8 - Prob. 101ECh. 2.8 - In Problems 99116, solve the inequality and...Ch. 2.8 - Prob. 103ECh. 2.8 - In Problems 99116, solve the inequality and...Ch. 2.8 - In Problems 99116, solve the inequality and...Ch. 2.8 - Prob. 106ECh. 2.8 - Prob. 107ECh. 2.8 - Prob. 108ECh. 2.8 - Prob. 109ECh. 2.8 - Prob. 110ECh. 2.8 - Prob. 111ECh. 2.8 - Prob. 112ECh. 2.8 - Prob. 113ECh. 2.8 - In Problems 99116, solve the inequality and...Ch. 2.8 - Prob. 115ECh. 2.8 - Prob. 116ECh. 2.8 - Auto Rental A car can be rented from Certified...Ch. 2.8 - Truck Rental A truck can be rented from Acme Truck...Ch. 2.8 - Prob. 119ECh. 2.8 - Final Grade To earn an A in Mrs. Smiths elementary...Ch. 2.8 - Prob. 121ECh. 2.8 - Prob. 122ECh. 2.8 - Prob. 123ECh. 2.8 - Advertising A marketing firm found that the...Ch. 2.8 - Prob. 125ECh. 2.8 - Delivery Service A messenger service charges 10 to...Ch. 2.8 - Prob. 127ECh. 2.8 - Compound inequalities are solved using the...Ch. 2.8 - Prob. 129ECh. 2.8 - Prob. 130ECh. 2.8 - Prob. 131ECh. 2.8 - Compound inequalities are solved using the...Ch. 2.8 - Prob. 133ECh. 2.8 - Prob. 134ECh. 2.8 - Prob. 135ECh. 2.8 - Prob. 136ECh. 2.8 - Prob. 137ECh. 2.8 - Prob. 138ECh. 2 - Determine whether the given value of the variable...Ch. 2 - Prob. 2PCTCh. 2 - Prob. 3PCTCh. 2 - Prob. 4PCTCh. 2 - Prob. 5PCTCh. 2 - Prob. 6PCTCh. 2 - Prob. 7PCTCh. 2 - Prob. 8PCTCh. 2 - Prob. 9PCTCh. 2 - Prob. 10PCTCh. 2 - Prob. 11PCTCh. 2 - Prob. 12PCTCh. 2 - Prob. 13PCTCh. 2 - Prob. 14PCTCh. 2 - Prob. 15PCTCh. 2 - Prob. 16PCTCh. 2 - Prob. 17PCTCh. 2 - Prob. 18PCTCh. 2 - Prob. 1RECh. 2 - Prob. 2RECh. 2 - Prob. 3RECh. 2 - Prob. 4RECh. 2 - Prob. 5RECh. 2 - Prob. 6RECh. 2 - Prob. 7RECh. 2 - Prob. 8RECh. 2 - Prob. 9RECh. 2 - Prob. 10RECh. 2 - Chapter 2 Review In Problems 518, solve the...Ch. 2 - Prob. 12RECh. 2 - Prob. 13RECh. 2 - Prob. 14RECh. 2 - Prob. 15RECh. 2 - Prob. 16RECh. 2 - Prob. 17RECh. 2 - Prob. 18RECh. 2 - Prob. 19RECh. 2 - Prob. 20RECh. 2 - Prob. 21RECh. 2 - Prob. 22RECh. 2 - Prob. 23RECh. 2 - Prob. 24RECh. 2 - Section 2.2 Linear Equations: Using the Properties...Ch. 2 - Section 2.2 Linear Equations: Using the Properties...Ch. 2 - Section 2.2 Linear Equations: Using the Properties...Ch. 2 - Section 2.2 Linear Equations: Using the Properties...Ch. 2 - Prob. 29RECh. 2 - Prob. 30RECh. 2 - Section 2.2 Linear Equations: Using the Properties...Ch. 2 - Prob. 32RECh. 2 - Prob. 33RECh. 2 - Prob. 34RECh. 2 - Prob. 35RECh. 2 - Prob. 36RECh. 2 - Prob. 37RECh. 2 - Prob. 38RECh. 2 - Prob. 39RECh. 2 - Prob. 40RECh. 2 - In Problems 37-48, solve the equation. Check your...Ch. 2 - Prob. 42RECh. 2 - In Problems 37-48, solve the equation. Check your...Ch. 2 - Prob. 44RECh. 2 - Prob. 45RECh. 2 - Prob. 46RECh. 2 - Prob. 47RECh. 2 - Prob. 48RECh. 2 - Prob. 49RECh. 2 - Prob. 50RECh. 2 - Prob. 51RECh. 2 - Prob. 52RECh. 2 - Prob. 53RECh. 2 - Prob. 54RECh. 2 - Prob. 55RECh. 2 - Prob. 56RECh. 2 - Prob. 57RECh. 2 - Prob. 58RECh. 2 - Prob. 59RECh. 2 - Prob. 60RECh. 2 - Prob. 61RECh. 2 - Prob. 62RECh. 2 - Prob. 63RECh. 2 - Prob. 64RECh. 2 - Prob. 65RECh. 2 - Prob. 66RECh. 2 - Prob. 67RECh. 2 - Prob. 68RECh. 2 - Prob. 69RECh. 2 - Prob. 70RECh. 2 - In Problems 7176, translate each phrase into an...Ch. 2 - Prob. 72RECh. 2 - Prob. 73RECh. 2 - Prob. 74RECh. 2 - Prob. 75RECh. 2 - Prob. 76RECh. 2 - Prob. 77RECh. 2 - Prob. 78RECh. 2 - Prob. 79RECh. 2 - Prob. 80RECh. 2 - Prob. 81RECh. 2 - Prob. 82RECh. 2 - Prob. 83RECh. 2 - Prob. 84RECh. 2 - Prob. 85RECh. 2 - Prob. 86RECh. 2 - Losing Weight Over the past year Lee Lai lost 28...Ch. 2 - Prob. 88RECh. 2 - Prob. 89RECh. 2 - Prob. 90RECh. 2 - Prob. 91RECh. 2 - Prob. 92RECh. 2 - Prob. 93RECh. 2 - Prob. 94RECh. 2 - Prob. 95RECh. 2 - Prob. 96RECh. 2 - Prob. 97RECh. 2 - Prob. 98RECh. 2 - Prob. 99RECh. 2 - Prob. 100RECh. 2 - Prob. 101RECh. 2 - Prob. 102RECh. 2 - Prob. 103RECh. 2 - Prob. 104RECh. 2 - Prob. 105RECh. 2 - Prob. 106RECh. 2 - Garden The perimeter of a rectangular garden is...Ch. 2 - Prob. 108RECh. 2 - Prob. 109RECh. 2 - Prob. 110RECh. 2 - Prob. 111RECh. 2 - Prob. 112RECh. 2 - Prob. 113RECh. 2 - Prob. 114RECh. 2 - Prob. 115RECh. 2 - Prob. 116RECh. 2 - Prob. 117RECh. 2 - Prob. 118RECh. 2 - Prob. 119RECh. 2 - Prob. 120RECh. 2 - Prob. 121RECh. 2 - Prob. 122RECh. 2 - Prob. 123RECh. 2 - Prob. 124RECh. 2 - Prob. 125RECh. 2 - Prob. 126RECh. 2 - Prob. 127RECh. 2 - Prob. 128RECh. 2 - Prob. 129RECh. 2 - Prob. 130RECh. 2 - Prob. 1TCh. 2 - Prob. 2TCh. 2 - Prob. 3TCh. 2 - Prob. 4TCh. 2 - Prob. 5TCh. 2 - Prob. 6TCh. 2 - Prob. 7TCh. 2 - Prob. 8TCh. 2 - Prob. 9TCh. 2 - Prob. 10TCh. 2 - Prob. 11TCh. 2 - Prob. 12TCh. 2 - Prob. 13TCh. 2 - Prob. 14TCh. 2 - Prob. 15TCh. 2 - Prob. 16TCh. 2 - Prob. 17TCh. 2 - Prob. 18TCh. 2 - Prob. 19TCh. 2 - Prob. 20T
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