Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN: 9780079039897
Author: Carter
Publisher: McGraw Hill
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Chapter 2.3, Problem 55HP

(a)

To determine

Solve the equation a+45+a  =  1 for a .

(a)

Expert Solution
Check Mark

Answer to Problem 55HP

  No solution

Explanation of Solution

Given:

The equation a+45+a  =  1

Concept Used:

Addition or Subtraction Property of Equality:

If a  =  b , then a + c =  b + c or If a  =  b , then a − c =  b − c

The property that states that if you add or subtract the same number to both sides of an equation, the sides remain equal (i.e., the equation continues to be true.)

Multiplication and Division Properties of Equality:

If a  =  b , then a · c  =  b · c

If a  =  b , then a ÷ c  =  b ÷ c , where c is not equal to 0.

In other words, if two expressions are equal to each other and you multiply or divide (except for 0) the exact same constant to both sides, the two sides will remain equal. 

Calculation:

The equation: a+45+a  =  1

Step1: Use the cross multiplication method: ab=cd⇒a  ·  d=b  ·  c

Solve: a+4=1  ·  (5+a)a+4=5+aa−a+4=5+a−a  [ Subtract a from  both  sides ]4≠5

In an equation the variable term in the left side and right side are same, the equation has no solutions (if no value of the variable makes the equation true).

Inconsistent equations: No solutions

For example, 3=3 is an identity equation. An equation like 3=5 is an inconsistent equation, since 3 is not equal to 5. If in the process of solving an equation we end up with an inconsistent equation, then the original equation has no solutions.

Thus, the solution of the equation a+45+a  =  1 has No solution

(b)

To determine

Solve the equation 1+b1−b  =  1

(b)

Expert Solution
Check Mark

Answer to Problem 55HP

Has a solution; b=0

Explanation of Solution

Given:

The equation: 1+b1−b  =  1

Concept Used:

Addition or Subtraction Property of Equality:

If a  =  b , then a + c =  b + c or If a  =  b , then a − c =  b − c

The property that states that if you add or subtract the same number to both sides of an equation, the sides remain equal (i.e., the equation continues to be true.)

Multiplication and Division Properties of Equality:

If a  =  b , then a · c  =  b · c

If a  =  b , then a ÷ c  =  b ÷ c , where c is not equal to 0.

In other words, if two expressions are equal to each other and you multiply or divide (except for 0) the exact same constant to both sides, the two sides will remain equal. 

Calculation:

Step1: Use the cross multiplication method: ab=cd⇒a  ·  d=b  ·  c

The equation: 1+b1−b  =  1

Solve: 1+b=1  ·  (1−b)  [  Rule  ab=cd⇒a  ·  d=b  ·  c]1+b=1−b1+b+b=1−b+b  [ Add  to b both  sides ]  1+2b=11−1+2b=1−1  [ Subtract  from  both  sides ]2b=02b2=02  [ Divide  both  sides  by  2] b=0 Check  the  solution  when  b=01+b1−b  =  11+01−0  =  111  =  11=1  (checked)

Thus, the solution of the equation 1+b1−b  =  1 has a solution b=0

(c)

To determine

Solve the equation c−55−c  =  1

(c)

Expert Solution
Check Mark

Answer to Problem 55HP

  No  Solution.

Explanation of Solution

Given:

The equation: c−55−c  =  1

Concept Used:

Addition or Subtraction Property of Equality:

If a  =  b , then a + c =  b + c or If a  =  b , then a − c =  b − c

The property that states that if you add or subtract the same number to both sides of an equation, the sides remain equal (i.e., the equation continues to be true.)

Multiplication and Division Properties of Equality:

If a  =  b , then a · c  =  b · c

If a  =  b , then a ÷ c  =  b ÷ c , where c is not equal to 0.

In other words, if two expressions are equal to each other and you multiply or divide (except for 0) the exact same constant to both sides, the two sides will remain equal. 

Calculation:

The equation: c−55−c  =  1

Solve: c−5−(c−5)  =  1  [  Rule:  b−a=−  (a−b)  ]−  c−5(c−5)  =  1   −1  ≠  1  No  Solution.

Inconsistent equations: No solutions

For example, 3=3 is an identity equation. An equation like 3=5 is an inconsistent equation, since 3 is not equal to 5. If in the process of solving an equation we end up with an inconsistent equation, then the original equation has no solutions.

Thus, the solution of the equation c−55−c  =  1 has No  Solution.

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Chapter 2.3, Problem 54HP
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Chapter 2.3, Problem 56HP

Chapter 2 Solutions

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

Ch. 2.1 - Prob. 1AGPCh. 2.1 - Prob. 1BGPCh. 2.1 - Prob. 2GPCh. 2.1 - Prob. 3GPCh. 2.1 - Prob. 4AGPCh. 2.1 - Prob. 4BGPCh. 2.1 - Prob. 5GPCh. 2.1 - Prob. 1CYUCh. 2.1 - Prob. 2CYUCh. 2.1 - Prob. 3CYU
Ch. 2.1 - Prob. 4CYUCh. 2.1 - Prob. 5CYUCh. 2.1 - Prob. 6CYUCh. 2.1 - Prob. 7CYUCh. 2.1 - Prob. 8CYUCh. 2.1 - Prob. 9CYUCh. 2.1 - Prob. 10CYUCh. 2.1 - Prob. 11CYUCh. 2.1 - Prob. 12CYUCh. 2.1 - Prob. 13CYUCh. 2.1 - Prob. 14CYUCh. 2.1 - Prob. 15CYUCh. 2.1 - Prob. 16CYUCh. 2.1 - Prob. 17CYUCh. 2.1 - Prob. 18CYUCh. 2.1 - Prob. 19CYUCh. 2.1 - Prob. 20CYUCh. 2.1 - Prob. 21PPSCh. 2.1 - Prob. 22PPSCh. 2.1 - Prob. 23PPSCh. 2.1 - Prob. 24PPSCh. 2.1 - Prob. 25PPSCh. 2.1 - Prob. 26PPSCh. 2.1 - Prob. 27PPSCh. 2.1 - Prob. 28PPSCh. 2.1 - Prob. 29PPSCh. 2.1 - Prob. 30PPSCh. 2.1 - Prob. 31PPSCh. 2.1 - Prob. 32PPSCh. 2.1 - Prob. 33PPSCh. 2.1 - Prob. 34PPSCh. 2.1 - Prob. 35PPSCh. 2.1 - Prob. 36PPSCh. 2.1 - Prob. 37PPSCh. 2.1 - Prob. 38PPSCh. 2.1 - Prob. 39PPSCh. 2.1 - Prob. 40PPSCh. 2.1 - Prob. 41PPSCh. 2.1 - Prob. 42PPSCh. 2.1 - Prob. 43PPSCh. 2.1 - Prob. 44PPSCh. 2.1 - Prob. 45PPSCh. 2.1 - Prob. 46PPSCh. 2.1 - Prob. 47HPCh. 2.1 - Prob. 48HPCh. 2.1 - Prob. 49HPCh. 2.1 - Prob. 50HPCh. 2.1 - Prob. 51PFACh. 2.1 - Prob. 52PFACh. 2.1 - Prob. 53PFACh. 2.1 - Prob. 54PFACh. 2.1 - Prob. 55PFACh. 2.1 - Prob. 56PFACh. 2.2 - Prob. 1AGPCh. 2.2 - Prob. 1BGPCh. 2.2 - Prob. 2AGPCh. 2.2 - Prob. 2BGPCh. 2.2 - Prob. 3AGPCh. 2.2 - Prob. 3BGPCh. 2.2 - Prob. 4GPCh. 2.2 - Prob. 1CYUCh. 2.2 - Prob. 2CYUCh. 2.2 - Prob. 3CYUCh. 2.2 - Prob. 4CYUCh. 2.2 - Prob. 5CYUCh. 2.2 - Prob. 6CYUCh. 2.2 - Prob. 7CYUCh. 2.2 - Prob. 8CYUCh. 2.2 - Prob. 9CYUCh. 2.2 - Prob. 10CYUCh. 2.2 - Prob. 11CYUCh. 2.2 - Prob. 12CYUCh. 2.2 - Prob. 13CYUCh. 2.2 - Prob. 14CYUCh. 2.2 - Prob. 15CYUCh. 2.2 - Prob. 16CYUCh. 2.2 - Prob. 17CYUCh. 2.2 - Prob. 18PPSCh. 2.2 - Prob. 19PPSCh. 2.2 - Prob. 20PPSCh. 2.2 - Prob. 21PPSCh. 2.2 - Prob. 22PPSCh. 2.2 - Prob. 23PPSCh. 2.2 - Prob. 24PPSCh. 2.2 - Prob. 25PPSCh. 2.2 - Prob. 26PPSCh. 2.2 - Prob. 27PPSCh. 2.2 - Prob. 28PPSCh. 2.2 - Prob. 29PPSCh. 2.2 - Prob. 30PPSCh. 2.2 - Prob. 31PPSCh. 2.2 - Prob. 32PPSCh. 2.2 - Prob. 33PPSCh. 2.2 - Prob. 34PPSCh. 2.2 - Prob. 35PPSCh. 2.2 - Prob. 36PPSCh. 2.2 - Prob. 37PPSCh. 2.2 - 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Prob. 12CYUCh. 2.5 - Prob. 13PPSCh. 2.5 - Prob. 14PPSCh. 2.5 - Prob. 15PPSCh. 2.5 - Prob. 16PPSCh. 2.5 - Prob. 17PPSCh. 2.5 - Prob. 18PPSCh. 2.5 - Prob. 19PPSCh. 2.5 - Prob. 20PPSCh. 2.5 - Prob. 21PPSCh. 2.5 - Prob. 22PPSCh. 2.5 - Prob. 23PPSCh. 2.5 - Prob. 24PPSCh. 2.5 - Prob. 25PPSCh. 2.5 - Prob. 26PPSCh. 2.5 - Prob. 27PPSCh. 2.5 - Prob. 28PPSCh. 2.5 - Prob. 29PPSCh. 2.5 - Prob. 30PPSCh. 2.5 - Prob. 31PPSCh. 2.5 - Prob. 32PPSCh. 2.5 - Prob. 33PPSCh. 2.5 - Prob. 34PPSCh. 2.5 - Prob. 35PPSCh. 2.5 - Prob. 36PPSCh. 2.5 - Prob. 37PPSCh. 2.5 - Prob. 38PPSCh. 2.5 - Prob. 39PPSCh. 2.5 - Prob. 40PPSCh. 2.5 - Prob. 41PPSCh. 2.5 - Prob. 42PPSCh. 2.5 - Prob. 43PPSCh. 2.5 - Prob. 44PPSCh. 2.5 - Prob. 45PPSCh. 2.5 - Prob. 46PPSCh. 2.5 - Prob. 47PPSCh. 2.5 - Prob. 48PPSCh. 2.5 - Prob. 49PPSCh. 2.5 - Prob. 50PPSCh. 2.5 - Prob. 51PPSCh. 2.5 - Prob. 52PPSCh. 2.5 - Prob. 53PPSCh. 2.5 - Prob. 54PPSCh. 2.5 - Prob. 55PPSCh. 2.5 - Prob. 56HPCh. 2.5 - Prob. 57HPCh. 2.5 - Prob. 58HPCh. 2.5 - Prob. 59HPCh. 2.5 - 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Prob. 8PPSCh. 2.7 - Prob. 9PPSCh. 2.7 - Prob. 10PPSCh. 2.7 - Prob. 11PPSCh. 2.7 - Prob. 12PPSCh. 2.7 - Prob. 13PPSCh. 2.7 - Prob. 14PPSCh. 2.7 - Prob. 15PPSCh. 2.7 - Prob. 16PPSCh. 2.7 - Prob. 17PPSCh. 2.7 - Prob. 18PPSCh. 2.7 - Prob. 19PPSCh. 2.7 - Prob. 20PPSCh. 2.7 - Prob. 21PPSCh. 2.7 - Prob. 22PPSCh. 2.7 - Prob. 23PPSCh. 2.7 - Prob. 24PPSCh. 2.7 - Prob. 25PPSCh. 2.7 - Prob. 26PPSCh. 2.7 - Prob. 27PPSCh. 2.7 - Prob. 28PPSCh. 2.7 - Prob. 29PPSCh. 2.7 - Prob. 30PPSCh. 2.7 - Prob. 31PPSCh. 2.7 - Prob. 32PPSCh. 2.7 - Prob. 33PPSCh. 2.7 - Prob. 34PPSCh. 2.7 - Prob. 35HPCh. 2.7 - Prob. 36HPCh. 2.7 - Prob. 37HPCh. 2.7 - Prob. 38HPCh. 2.7 - Prob. 39HPCh. 2.7 - Prob. 40HPCh. 2.7 - Prob. 41PFACh. 2.7 - Prob. 42PFACh. 2.7 - Prob. 43PFACh. 2.7 - Prob. 44PFACh. 2.7 - Prob. 45PFACh. 2.7 - Prob. 46PFACh. 2.7 - Prob. 47PFACh. 2.7 - Prob. 48PFACh. 2.7 - Prob. 49PFACh. 2 - Prob. 1SGRCh. 2 - Prob. 2SGRCh. 2 - Prob. 3SGRCh. 2 - Prob. 4SGRCh. 2 - Prob. 5SGRCh. 2 - Prob. 6SGRCh. 2 - Prob. 7SGRCh. 2 - Prob. 8SGRCh. 2 - Prob. 9SGRCh. 2 - Prob. 10SGRCh. 2 - Prob. 11SGRCh. 2 - Prob. 12SGRCh. 2 - Prob. 13SGRCh. 2 - Prob. 14SGRCh. 2 - Prob. 15SGRCh. 2 - Prob. 16SGRCh. 2 - Prob. 17SGRCh. 2 - Prob. 18SGRCh. 2 - Prob. 19SGRCh. 2 - Prob. 20SGRCh. 2 - Prob. 21SGRCh. 2 - Prob. 22SGRCh. 2 - Prob. 23SGRCh. 2 - Prob. 24SGRCh. 2 - Prob. 25SGRCh. 2 - Prob. 26SGRCh. 2 - Prob. 27SGRCh. 2 - Prob. 28SGRCh. 2 - Prob. 29SGRCh. 2 - Prob. 30SGRCh. 2 - Prob. 31SGRCh. 2 - Prob. 32SGRCh. 2 - Prob. 33SGRCh. 2 - Prob. 34SGRCh. 2 - Prob. 35SGRCh. 2 - Prob. 36SGRCh. 2 - Prob. 37SGRCh. 2 - Prob. 38SGRCh. 2 - Prob. 39SGRCh. 2 - Prob. 40SGRCh. 2 - Prob. 41SGRCh. 2 - Prob. 42SGRCh. 2 - Prob. 43SGRCh. 2 - Prob. 44SGRCh. 2 - Prob. 45SGRCh. 2 - Prob. 46SGRCh. 2 - Prob. 47SGRCh. 2 - Prob. 48SGRCh. 2 - Prob. 49SGRCh. 2 - Prob. 50SGRCh. 2 - Prob. 51SGRCh. 2 - Prob. 52SGRCh. 2 - Prob. 53SGRCh. 2 - Prob. 54SGRCh. 2 - Prob. 55SGRCh. 2 - Prob. 56SGRCh. 2 - Prob. 57SGRCh. 2 - Prob. 58SGRCh. 2 - Prob. 59SGRCh. 2 - Prob. 60SGRCh. 2 - Prob. 61SGRCh. 2 - Prob. 62SGRCh. 2 - Prob. 63SGRCh. 2 - Prob. 64SGRCh. 2 - Prob. 65SGRCh. 2 - Prob. 66SGRCh. 2 - Prob. 67SGRCh. 2 - Prob. 68SGRCh. 2 - Prob. 69SGRCh. 2 - Prob. 70SGRCh. 2 - Prob. 71SGRCh. 2 - Prob. 72SGRCh. 2 - Prob. 73SGRCh. 2 - Prob. 74SGRCh. 2 - Prob. 75SGRCh. 2 - Prob. 76SGRCh. 2 - Prob. 77SGRCh. 2 - Prob. 78SGRCh. 2 - Prob. 79SGRCh. 2 - Prob. 1PTCh. 2 - Prob. 2PTCh. 2 - Prob. 3PTCh. 2 - Prob. 4PTCh. 2 - Prob. 5PTCh. 2 - Prob. 6PTCh. 2 - Prob. 7PTCh. 2 - Prob. 8PTCh. 2 - Prob. 9PTCh. 2 - Prob. 10PTCh. 2 - Prob. 11PTCh. 2 - Prob. 12PTCh. 2 - Prob. 13PTCh. 2 - Prob. 14PTCh. 2 - Prob. 15PTCh. 2 - Prob. 16PTCh. 2 - Prob. 17PTCh. 2 - Prob. 18PTCh. 2 - Prob. 19PTCh. 2 - Prob. 20PTCh. 2 - Prob. 21PTCh. 2 - Prob. 22PTCh. 2 - Prob. 23PTCh. 2 - Prob. 24PTCh. 2 - Prob. 25PTCh. 2 - Prob. 1PFACh. 2 - Prob. 2PFACh. 2 - Prob. 3PFACh. 2 - Prob. 4PFACh. 2 - Prob. 5PFACh. 2 - Prob. 6PFACh. 2 - Prob. 7PFACh. 2 - Prob. 8PFACh. 2 - Prob. 9PFACh. 2 - Prob. 10PFACh. 2 - Prob. 11PFACh. 2 - Prob. 12PFACh. 2 - Prob. 13PFACh. 2 - Prob. 14PFACh. 2 - Prob. 15PFA

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