Algebra 2
Algebra 2
1st Edition
ISBN: 9780078884825
Author: McGraw-Hill/Glencoe
Publisher: Glencoe/McGraw-Hill School Pub Co
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Concept explainers

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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Question
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Chapter 1.4, Problem 46HP
To determine

To solve: the given equation.

Expert Solution & Answer
Check Mark

Answer to Problem 46HP

The result is x∈{−1,1} .

Explanation of Solution

Given information:

Given equation is

  |2x−1|+3=|5−x|

Calculation:

In order to clear the absolute value bar, write all the possibilities:

  |2x−1|={−2x+1, 2x−1<02x−1,  2x−1≥0|5−x|={−5+x,  5−x<05−x,  5−x≥0

Therefore,

  |2x−1|={−2x+1, x<122x−1,  x≥12|5−x|={−5+x,  x>55−x,  x≤5

The following key points and interval

  (12,5)(−∞,12),[12,5],(5,∞)

Solve the equation on given interval x∈(−∞,12) ,

Now solve the equation,

  −2x+1+3=5−x−2x+4+2x=5−x+2x4=5+xx=−1

Now, check the solution is in the interval (−∞,12) .

Solve the equation on given interval x∈[12,5] .

Now, solve the equation

  2x−1+3=5−x2x+2+x=5−x+x3x=3x=1

Now, check the solution is in the interval [12,5]

  1∈[12,5]

Solve the equation of the given interval x∈(5,∞)

Now, solve the equation

  2x−1+3=−5+x2x+2−x=5+x−xx+2=−5x=−7

Now, check the solution is in the interval (5,∞) .

  −7∈(5,∞)

Hence, the result is x∈{−1,1} .

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Chapter 1.4, Problem 45HP
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Chapter 1 Solutions

Algebra 2

Ch. 1.1 - Prob. 1ACYPCh. 1.1 - Prob. 1BCYPCh. 1.1 - Prob. 2ACYPCh. 1.1 - Prob. 2BCYPCh. 1.1 - Prob. 2CCYPCh. 1.1 - Prob. 3CYPCh. 1.1 - Prob. 1CYUCh. 1.1 - Prob. 2CYUCh. 1.1 - Prob. 3CYUCh. 1.1 - Prob. 4CYU
Ch. 1.1 - Prob. 5CYUCh. 1.1 - Prob. 6CYUCh. 1.1 - Prob. 7CYUCh. 1.1 - Prob. 8CYUCh. 1.1 - Prob. 9CYUCh. 1.1 - Prob. 10CYUCh. 1.1 - Prob. 11PPSCh. 1.1 - Prob. 12PPSCh. 1.1 - Prob. 13PPSCh. 1.1 - Prob. 14PPSCh. 1.1 - Prob. 15PPSCh. 1.1 - Prob. 16PPSCh. 1.1 - Prob. 17PPSCh. 1.1 - Prob. 18PPSCh. 1.1 - Prob. 19PPSCh. 1.1 - Prob. 20PPSCh. 1.1 - Prob. 21PPSCh. 1.1 - Prob. 22PPSCh. 1.1 - Prob. 23PPSCh. 1.1 - Prob. 24PPSCh. 1.1 - Prob. 25PPSCh. 1.1 - Prob. 26PPSCh. 1.1 - Prob. 27PPSCh. 1.1 - Prob. 28PPSCh. 1.1 - Prob. 29PPSCh. 1.1 - Prob. 30PPSCh. 1.1 - Prob. 31PPSCh. 1.1 - Prob. 32PPSCh. 1.1 - Prob. 33PPSCh. 1.1 - Prob. 34PPSCh. 1.1 - Prob. 35PPSCh. 1.1 - Prob. 36PPSCh. 1.1 - Prob. 37PPSCh. 1.1 - Prob. 38PPSCh. 1.1 - Prob. 39PPSCh. 1.1 - Prob. 40PPSCh. 1.1 - Prob. 41PPSCh. 1.1 - Prob. 42PPSCh. 1.1 - Prob. 43HPCh. 1.1 - Prob. 44HPCh. 1.1 - Prob. 45HPCh. 1.1 - Prob. 46HPCh. 1.1 - Prob. 47HPCh. 1.1 - Prob. 48HPCh. 1.1 - Prob. 49HPCh. 1.1 - Prob. 50HPCh. 1.1 - Prob. 51HPCh. 1.1 - Prob. 52HPCh. 1.1 - 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Prob. 75STPCh. 1.2 - Prob. 76STPCh. 1.2 - Prob. 77STPCh. 1.2 - Prob. 78STPCh. 1.2 - Prob. 79STPCh. 1.2 - Prob. 80STPCh. 1.2 - Prob. 81STPCh. 1.2 - Prob. 82SCh. 1.2 - Prob. 83SCh. 1.2 - Prob. 84SCh. 1.2 - Prob. 85SCh. 1.2 - Prob. 86SCh. 1.2 - Prob. 87SCh. 1.2 - Prob. 88SCh. 1.2 - Prob. 89SCh. 1.3 - Prob. 1ACYPCh. 1.3 - Prob. 1BCYPCh. 1.3 - Prob. 2ACYPCh. 1.3 - Prob. 2BCYPCh. 1.3 - Prob. 3CYPCh. 1.3 - Prob. 4ACYPCh. 1.3 - Prob. 4BCYPCh. 1.3 - Prob. 5ACYPCh. 1.3 - Prob. 5BCYPCh. 1.3 - Prob. 6CYPCh. 1.3 - Prob. 7CYPCh. 1.3 - Prob. 1CYUCh. 1.3 - Prob. 2CYUCh. 1.3 - Prob. 3CYUCh. 1.3 - Prob. 4CYUCh. 1.3 - Prob. 5CYUCh. 1.3 - Prob. 6CYUCh. 1.3 - Prob. 7CYUCh. 1.3 - Prob. 8CYUCh. 1.3 - Prob. 9CYUCh. 1.3 - Prob. 10CYUCh. 1.3 - Prob. 11CYUCh. 1.3 - Prob. 12CYUCh. 1.3 - Prob. 13CYUCh. 1.3 - Prob. 14CYUCh. 1.3 - Prob. 15CYUCh. 1.3 - Prob. 16CYUCh. 1.3 - Prob. 17CYUCh. 1.3 - Prob. 18CYUCh. 1.3 - Prob. 19CYUCh. 1.3 - Prob. 20CYUCh. 1.3 - Prob. 21CYUCh. 1.3 - Prob. 22PPSCh. 1.3 - Prob. 23PPSCh. 1.3 - 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Prob. 73STPCh. 1.3 - Prob. 74STPCh. 1.3 - Prob. 75SCh. 1.3 - Prob. 76SCh. 1.3 - Prob. 77SCh. 1.3 - Prob. 78SCh. 1.3 - Prob. 79SCh. 1.3 - Prob. 80SCh. 1.3 - Prob. 81SCh. 1.3 - Prob. 82SCh. 1.4 - Prob. 1ACYPCh. 1.4 - Prob. 1BCYPCh. 1.4 - Prob. 2ACYPCh. 1.4 - Prob. 2BCYPCh. 1.4 - Prob. 3ACYPCh. 1.4 - Prob. 3BCYPCh. 1.4 - Prob. 4ACYPCh. 1.4 - Prob. 4BCYPCh. 1.4 - Prob. 1CYUCh. 1.4 - Prob. 2CYUCh. 1.4 - Prob. 3CYUCh. 1.4 - Prob. 4CYUCh. 1.4 - Prob. 5CYUCh. 1.4 - Prob. 6CYUCh. 1.4 - Prob. 7CYUCh. 1.4 - Prob. 8CYUCh. 1.4 - Prob. 9CYUCh. 1.4 - Prob. 10CYUCh. 1.4 - Prob. 11CYUCh. 1.4 - Prob. 12CYUCh. 1.4 - Prob. 13CYUCh. 1.4 - Prob. 14PPSCh. 1.4 - Prob. 15PPSCh. 1.4 - Prob. 16PPSCh. 1.4 - Prob. 17PPSCh. 1.4 - Prob. 18PPSCh. 1.4 - Prob. 19PPSCh. 1.4 - Prob. 20PPSCh. 1.4 - Prob. 21PPSCh. 1.4 - Prob. 22PPSCh. 1.4 - Prob. 23PPSCh. 1.4 - Prob. 24PPSCh. 1.4 - Prob. 25PPSCh. 1.4 - Prob. 26PPSCh. 1.4 - Prob. 27PPSCh. 1.4 - Prob. 28PPSCh. 1.4 - Prob. 29PPSCh. 1.4 - Prob. 30PPSCh. 1.4 - Prob. 31PPSCh. 1.4 - Prob. 32PPSCh. 1.4 - Prob. 33PPSCh. 1.4 - Prob. 34PPSCh. 1.4 - Prob. 35PPSCh. 1.4 - Prob. 36PPSCh. 1.4 - Prob. 37PPSCh. 1.4 - Prob. 38PPSCh. 1.4 - Prob. 39PPSCh. 1.4 - Prob. 40PPSCh. 1.4 - Prob. 41PPSCh. 1.4 - Prob. 42PPSCh. 1.4 - Prob. 43PPSCh. 1.4 - Prob. 44PPSCh. 1.4 - Prob. 45HPCh. 1.4 - Prob. 46HPCh. 1.4 - Prob. 47HPCh. 1.4 - Prob. 48HPCh. 1.4 - Prob. 49HPCh. 1.4 - Prob. 50HPCh. 1.4 - Prob. 51HPCh. 1.4 - Prob. 52HPCh. 1.4 - Prob. 53HPCh. 1.4 - Prob. 54HPCh. 1.4 - Prob. 55HPCh. 1.4 - Prob. 56STPCh. 1.4 - Prob. 57STPCh. 1.4 - Prob. 58STPCh. 1.4 - Prob. 59STPCh. 1.4 - Prob. 60STPCh. 1.4 - Prob. 61STPCh. 1.4 - Prob. 62STPCh. 1.4 - Prob. 63STPCh. 1.4 - Prob. 64STPCh. 1.4 - Prob. 65STPCh. 1.4 - Prob. 66STPCh. 1.4 - Prob. 67STPCh. 1.4 - Prob. 68STPCh. 1.4 - Prob. 69SCh. 1.4 - Prob. 70SCh. 1.4 - Prob. 71SCh. 1.4 - Prob. 72SCh. 1.4 - Prob. 73SCh. 1.4 - Prob. 74SCh. 1.5 - Prob. 1ACYPCh. 1.5 - Prob. 1BCYPCh. 1.5 - Prob. 2ACYPCh. 1.5 - Prob. 2BCYPCh. 1.5 - Prob. 3ACYPCh. 1.5 - Prob. 3BCYPCh. 1.5 - Prob. 3CCYPCh. 1.5 - Prob. 3DCYPCh. 1.5 - Prob. 4CYPCh. 1.5 - Prob. 1CYUCh. 1.5 - Prob. 2CYUCh. 1.5 - Prob. 3CYUCh. 1.5 - Prob. 4CYUCh. 1.5 - Prob. 5CYUCh. 1.5 - Prob. 6CYUCh. 1.5 - Prob. 7CYUCh. 1.5 - Prob. 8CYUCh. 1.5 - Prob. 9CYUCh. 1.5 - Prob. 10PPSCh. 1.5 - Prob. 11PPSCh. 1.5 - Prob. 12PPSCh. 1.5 - Prob. 13PPSCh. 1.5 - Prob. 14PPSCh. 1.5 - Prob. 15PPSCh. 1.5 - Prob. 16PPSCh. 1.5 - Prob. 17PPSCh. 1.5 - Prob. 18PPSCh. 1.5 - Prob. 19PPSCh. 1.5 - Prob. 20PPSCh. 1.5 - Prob. 21PPSCh. 1.5 - Prob. 22PPSCh. 1.5 - Prob. 23PPSCh. 1.5 - Prob. 24PPSCh. 1.5 - Prob. 25PPSCh. 1.5 - Prob. 26PPSCh. 1.5 - Prob. 27PPSCh. 1.5 - Prob. 28PPSCh. 1.5 - Prob. 29PPSCh. 1.5 - Prob. 30PPSCh. 1.5 - Prob. 31PPSCh. 1.5 - Prob. 32PPSCh. 1.5 - Prob. 33PPSCh. 1.5 - Prob. 34PPSCh. 1.5 - Prob. 35PPSCh. 1.5 - Prob. 36PPSCh. 1.5 - Prob. 37PPSCh. 1.5 - Prob. 38PPSCh. 1.5 - Prob. 39PPSCh. 1.5 - Prob. 40PPSCh. 1.5 - Prob. 41PPSCh. 1.5 - Prob. 42PPSCh. 1.5 - Prob. 43PPSCh. 1.5 - Prob. 44HPCh. 1.5 - Prob. 45HPCh. 1.5 - Prob. 46HPCh. 1.5 - Prob. 47HPCh. 1.5 - Prob. 48HPCh. 1.5 - Prob. 49HPCh. 1.5 - Prob. 50HPCh. 1.5 - Prob. 51HPCh. 1.5 - Prob. 52HPCh. 1.5 - Prob. 53HPCh. 1.5 - Prob. 54STPCh. 1.5 - Prob. 55STPCh. 1.5 - Prob. 56STPCh. 1.5 - Prob. 57STPCh. 1.5 - Prob. 58STPCh. 1.5 - Prob. 59STPCh. 1.5 - Prob. 60STPCh. 1.5 - Prob. 61SCh. 1.5 - Prob. 62SCh. 1.5 - Prob. 63SCh. 1.5 - Prob. 64SCh. 1.5 - Prob. 65SCh. 1.5 - Prob. 66SCh. 1.5 - Prob. 1ECh. 1.5 - Prob. 2ECh. 1.5 - Prob. 3ECh. 1.5 - Prob. 4ECh. 1.5 - Prob. 5ECh. 1.5 - Prob. 6ECh. 1.5 - Prob. 7ECh. 1.5 - Prob. 8ECh. 1.5 - Prob. 9ECh. 1.5 - Prob. 10ECh. 1.5 - Prob. 11ECh. 1.5 - Prob. 12ECh. 1.5 - Prob. 13ECh. 1.5 - Prob. 14ECh. 1.5 - Prob. 15ECh. 1.5 - Prob. 16ECh. 1.5 - Prob. 17ECh. 1.5 - Prob. 18ECh. 1.6 - Prob. 1ACYPCh. 1.6 - Prob. 1BCYPCh. 1.6 - Prob. 2ACYPCh. 1.6 - Prob. 2BCYPCh. 1.6 - Prob. 3ACYPCh. 1.6 - Prob. 3BCYPCh. 1.6 - Prob. 3CCYPCh. 1.6 - Prob. 3DCYPCh. 1.6 - Prob. 4ACYPCh. 1.6 - Prob. 4BCYPCh. 1.6 - Prob. 5CYPCh. 1.6 - Prob. 1CYUCh. 1.6 - Prob. 2CYUCh. 1.6 - Prob. 3CYUCh. 1.6 - Prob. 4CYUCh. 1.6 - Prob. 5CYUCh. 1.6 - Prob. 6CYUCh. 1.6 - Prob. 7CYUCh. 1.6 - Prob. 8CYUCh. 1.6 - Prob. 9CYUCh. 1.6 - Prob. 10CYUCh. 1.6 - Prob. 11CYUCh. 1.6 - Prob. 12PPSCh. 1.6 - Prob. 13PPSCh. 1.6 - Prob. 14PPSCh. 1.6 - Prob. 15PPSCh. 1.6 - Prob. 16PPSCh. 1.6 - Prob. 17PPSCh. 1.6 - Prob. 18PPSCh. 1.6 - Prob. 19PPSCh. 1.6 - Prob. 20PPSCh. 1.6 - Prob. 21PPSCh. 1.6 - Prob. 22PPSCh. 1.6 - Prob. 23PPSCh. 1.6 - Prob. 24PPSCh. 1.6 - Prob. 25PPSCh. 1.6 - Prob. 26PPSCh. 1.6 - Prob. 27PPSCh. 1.6 - Prob. 28PPSCh. 1.6 - Prob. 29PPSCh. 1.6 - Prob. 30PPSCh. 1.6 - Prob. 31PPSCh. 1.6 - Prob. 32PPSCh. 1.6 - Prob. 33PPSCh. 1.6 - Prob. 34PPSCh. 1.6 - Prob. 35PPSCh. 1.6 - Prob. 36PPSCh. 1.6 - Prob. 37PPSCh. 1.6 - Prob. 38PPSCh. 1.6 - Prob. 39PPSCh. 1.6 - Prob. 40PPSCh. 1.6 - Prob. 41PPSCh. 1.6 - Prob. 42PPSCh. 1.6 - Prob. 43PPSCh. 1.6 - Prob. 44PPSCh. 1.6 - Prob. 45PPSCh. 1.6 - Prob. 46PPSCh. 1.6 - Prob. 47PPSCh. 1.6 - Prob. 48PPSCh. 1.6 - Prob. 49PPSCh. 1.6 - Prob. 50PPSCh. 1.6 - 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Prob. 8MCQCh. 1 - Prob. 9MCQCh. 1 - Prob. 10MCQCh. 1 - Prob. 11MCQCh. 1 - Prob. 12MCQCh. 1 - Prob. 13MCQCh. 1 - Prob. 14MCQCh. 1 - Prob. 15MCQCh. 1 - Prob. 16MCQCh. 1 - Prob. 17MCQCh. 1 - Prob. 18MCQCh. 1 - Prob. 19MCQCh. 1 - Prob. 20MCQCh. 1 - Prob. 1SGRCh. 1 - Prob. 2SGRCh. 1 - Prob. 3SGRCh. 1 - Prob. 4SGRCh. 1 - Prob. 5SGRCh. 1 - Prob. 6SGRCh. 1 - Prob. 7SGRCh. 1 - Prob. 8SGRCh. 1 - Prob. 9SGRCh. 1 - Prob. 10SGRCh. 1 - Prob. 11SGRCh. 1 - Prob. 12SGRCh. 1 - Prob. 13SGRCh. 1 - Prob. 14SGRCh. 1 - Prob. 15SGRCh. 1 - Prob. 16SGRCh. 1 - Prob. 17SGRCh. 1 - Prob. 18SGRCh. 1 - Prob. 19SGRCh. 1 - Prob. 20SGRCh. 1 - Prob. 21SGRCh. 1 - Prob. 22SGRCh. 1 - Prob. 23SGRCh. 1 - Prob. 24SGRCh. 1 - Prob. 25SGRCh. 1 - Prob. 26SGRCh. 1 - Prob. 27SGRCh. 1 - Prob. 28SGRCh. 1 - Prob. 29SGRCh. 1 - Prob. 30SGRCh. 1 - Prob. 31SGRCh. 1 - Prob. 32SGRCh. 1 - Prob. 33SGRCh. 1 - Prob. 34SGRCh. 1 - Prob. 35SGRCh. 1 - Prob. 36SGRCh. 1 - Prob. 37SGRCh. 1 - Prob. 38SGRCh. 1 - Prob. 39SGRCh. 1 - Prob. 40SGRCh. 1 - Prob. 41SGRCh. 1 - Prob. 42SGRCh. 1 - Prob. 43SGRCh. 1 - Prob. 44SGRCh. 1 - Prob. 45SGRCh. 1 - Prob. 46SGRCh. 1 - Prob. 47SGRCh. 1 - Prob. 48SGRCh. 1 - Prob. 49SGRCh. 1 - Prob. 50SGRCh. 1 - Prob. 51SGRCh. 1 - Prob. 52SGRCh. 1 - Prob. 53SGRCh. 1 - Prob. 1PTCh. 1 - Prob. 2PTCh. 1 - Prob. 3PTCh. 1 - Prob. 4PTCh. 1 - Prob. 5PTCh. 1 - Prob. 6PTCh. 1 - Prob. 7PTCh. 1 - Prob. 8PTCh. 1 - Prob. 9PTCh. 1 - Prob. 10PTCh. 1 - Prob. 11PTCh. 1 - Prob. 12PTCh. 1 - Prob. 13PTCh. 1 - Prob. 14PTCh. 1 - Prob. 15PTCh. 1 - Prob. 16PTCh. 1 - Prob. 17PTCh. 1 - Prob. 18PTCh. 1 - Prob. 19PTCh. 1 - Prob. 20PTCh. 1 - Prob. 21PTCh. 1 - Prob. 22PTCh. 1 - Prob. 23PTCh. 1 - Prob. 24PTCh. 1 - Prob. 25PTCh. 1 - Prob. 1ECh. 1 - Prob. 2ECh. 1 - Prob. 3ECh. 1 - Prob. 4ECh. 1 - Prob. 5ECh. 1 - Prob. 6ECh. 1 - Prob. 1STPCh. 1 - Prob. 2STPCh. 1 - Prob. 3STPCh. 1 - Prob. 4STPCh. 1 - Prob. 5STPCh. 1 - Prob. 6STPCh. 1 - Prob. 7STPCh. 1 - Prob. 8STPCh. 1 - Prob. 9STPCh. 1 - Prob. 10STPCh. 1 - Prob. 11STPCh. 1 - Prob. 12STPCh. 1 - Prob. 13STPCh. 1 - Prob. 14STP

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Publisher:McGraw-Hill Education
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