Pre-Algebra Student Edition
Pre-Algebra Student Edition
1st Edition
ISBN: 9780078957734
Author: Glencoe/McGraw-Hill
Publisher: MCG
bartleby

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.
bartleby

Videos

Question
Book Icon
Chapter 5.5, Problem 55HP
To determine

To explain: The method to determine if the equation has no solution, one solution, or if all numbers are solutions.

Expert Solution & Answer
Check Mark

Answer to Problem 55HP

If we solve any equation and get a value for the variable then the equation has one solution

If we solve an equation and get a false result, then the equation has no solution.

If we solve an equation and get a true result, then the equation has infinitely many solution.

Explanation of Solution

Calculation:

While solving an equation either we can get a solution, no solution or infinitely many solutions. Let us discuss these three cases.

  1. The equation has one solution
    2. If we solve any equation and get a value for the variable then the equation has one solution. For example

      x+2=5x=5−2x=3

    Here, we can see that there is only one solution x=3

  2. The equation has no solution
    3. If we solve an equation and get a false result, then the equation has no solution.

    For example,

      2x+2=2x+52x−2x=5−20=3

    Since, 0≠3 hence, we end in a false result which means the equation has no solution

  3. The equation has infinitely many solutions
    4. If we solve an equation and get a true result, then the equation has infinitely many solution.

    For example,

      2x+2=2x+22x−2x=2−20=0

    Since, 0=0 is true hence, the equation has infinitely many solutions.

Previous
Chapter 5.5, Problem 54HP
Next
Chapter 5.5, Problem 56STP

Chapter 5 Solutions

Pre-Algebra Student Edition

Ch. 5.1 - Prob. 1GPCh. 5.1 - Prob. 2GPCh. 5.1 - Prob. 3GPCh. 5.1 - Prob. 4GPCh. 5.1 - Prob. 1CYUCh. 5.1 - Prob. 2CYUCh. 5.1 - Prob. 3CYUCh. 5.1 - Prob. 4PPSCh. 5.1 - Prob. 5PPSCh. 5.1 - Prob. 6PPS
Ch. 5.1 - Prob. 7PPSCh. 5.1 - Prob. 8PPSCh. 5.1 - Prob. 9PPSCh. 5.1 - Prob. 10PPSCh. 5.1 - Prob. 11PPSCh. 5.1 - Prob. 12PPSCh. 5.1 - Prob. 13PPSCh. 5.1 - Prob. 14PPSCh. 5.1 - Prob. 15PPSCh. 5.1 - Prob. 16PPSCh. 5.1 - Prob. 17PPSCh. 5.1 - Prob. 18PPSCh. 5.1 - Prob. 19PPSCh. 5.1 - Prob. 20PPSCh. 5.1 - Prob. 21PPSCh. 5.1 - Prob. 22PPSCh. 5.1 - Prob. 23PPSCh. 5.1 - Prob. 24PPSCh. 5.1 - Prob. 25HPCh. 5.1 - Prob. 26HPCh. 5.1 - Prob. 27HPCh. 5.1 - Prob. 28HPCh. 5.1 - Prob. 29STPCh. 5.1 - Prob. 30STPCh. 5.1 - Prob. 31STPCh. 5.1 - Prob. 32STPCh. 5.1 - Prob. 33SRCh. 5.1 - Prob. 34SRCh. 5.1 - Prob. 35SRCh. 5.1 - Prob. 36SRCh. 5.1 - Prob. 37SRCh. 5.1 - Prob. 38SRCh. 5.1 - Prob. 39SRCh. 5.1 - Prob. 40SRCh. 5.1 - Prob. 41SRCh. 5.1 - Prob. 42SCh. 5.1 - Prob. 43SCh. 5.1 - Prob. 44SCh. 5.2 - Prob. 1AGPCh. 5.2 - Prob. 1BGPCh. 5.2 - Prob. 2AGPCh. 5.2 - Prob. 2BGPCh. 5.2 - Prob. 3GPCh. 5.2 - Prob. 1CYUCh. 5.2 - Prob. 2CYUCh. 5.2 - Prob. 3CYUCh. 5.2 - Prob. 4CYUCh. 5.2 - Prob. 5CYUCh. 5.2 - Prob. 6CYUCh. 5.2 - Prob. 7CYUCh. 5.2 - Prob. 8PPSCh. 5.2 - Prob. 9PPSCh. 5.2 - Prob. 10PPSCh. 5.2 - Prob. 11PPSCh. 5.2 - Prob. 12PPSCh. 5.2 - Prob. 13PPSCh. 5.2 - Prob. 14PPSCh. 5.2 - Prob. 15PPSCh. 5.2 - Prob. 16PPSCh. 5.2 - Prob. 17PPSCh. 5.2 - Prob. 18PPSCh. 5.2 - Prob. 19PPSCh. 5.2 - Prob. 20PPSCh. 5.2 - Prob. 21PPSCh. 5.2 - Prob. 22PPSCh. 5.2 - Prob. 23PPSCh. 5.2 - Prob. 24PPSCh. 5.2 - Prob. 25PPSCh. 5.2 - Prob. 26PPSCh. 5.2 - Prob. 27PPSCh. 5.2 - Prob. 28PPSCh. 5.2 - Prob. 29PPSCh. 5.2 - Prob. 30HPCh. 5.2 - Prob. 31HPCh. 5.2 - Prob. 32HPCh. 5.2 - Prob. 33HPCh. 5.2 - Prob. 34HPCh. 5.2 - Prob. 35STPCh. 5.2 - Prob. 36STPCh. 5.2 - Prob. 37STPCh. 5.2 - Prob. 38STPCh. 5.2 - Prob. 39SRCh. 5.2 - Prob. 40SRCh. 5.2 - Prob. 41SRCh. 5.2 - Prob. 42SRCh. 5.2 - Prob. 43SRCh. 5.2 - Prob. 44SRCh. 5.2 - Prob. 45SRCh. 5.2 - Prob. 46SRCh. 5.2 - Prob. 47SCh. 5.2 - Prob. 48SCh. 5.2 - Prob. 49SCh. 5.3 - Prob. 1AGPCh. 5.3 - Prob. 1BGPCh. 5.3 - Prob. 2GPCh. 5.3 - Prob. 3AGPCh. 5.3 - Prob. 3BGPCh. 5.3 - Prob. 4AGPCh. 5.3 - Prob. 4BGPCh. 5.3 - Prob. 4CGPCh. 5.3 - Prob. 5AGPCh. 5.3 - Prob. 5BGPCh. 5.3 - Prob. 1CYUCh. 5.3 - Prob. 2CYUCh. 5.3 - Prob. 3CYUCh. 5.3 - Prob. 4CYUCh. 5.3 - Prob. 5CYUCh. 5.3 - Prob. 6CYUCh. 5.3 - Prob. 7CYUCh. 5.3 - Prob. 8CYUCh. 5.3 - Prob. 9CYUCh. 5.3 - Prob. 10CYUCh. 5.3 - Prob. 11CYUCh. 5.3 - Prob. 12PPSCh. 5.3 - Prob. 13PPSCh. 5.3 - Prob. 14PPSCh. 5.3 - Prob. 15PPSCh. 5.3 - Prob. 16PPSCh. 5.3 - Prob. 17PPSCh. 5.3 - Prob. 18PPSCh. 5.3 - Prob. 19PPSCh. 5.3 - Prob. 20PPSCh. 5.3 - Prob. 21PPSCh. 5.3 - Prob. 22PPSCh. 5.3 - Prob. 23PPSCh. 5.3 - Prob. 24PPSCh. 5.3 - Prob. 25PPSCh. 5.3 - Prob. 26PPSCh. 5.3 - Prob. 27PPSCh. 5.3 - Prob. 28PPSCh. 5.3 - Prob. 29PPSCh. 5.3 - Prob. 30PPSCh. 5.3 - Prob. 31PPSCh. 5.3 - Prob. 32PPSCh. 5.3 - Prob. 33PPSCh. 5.3 - Prob. 34PPSCh. 5.3 - Prob. 35PPSCh. 5.3 - Prob. 36PPSCh. 5.3 - Prob. 37PPSCh. 5.3 - Prob. 39HPCh. 5.3 - Prob. 41HPCh. 5.3 - Prob. 42HPCh. 5.3 - Prob. 43HPCh. 5.3 - Prob. 44STPCh. 5.3 - Prob. 45STPCh. 5.3 - Prob. 46STPCh. 5.3 - Prob. 47STPCh. 5.3 - Prob. 48SRCh. 5.3 - Prob. 49SRCh. 5.3 - Prob. 50SRCh. 5.3 - Prob. 51SRCh. 5.3 - Prob. 52SRCh. 5.3 - Prob. 53SRCh. 5.3 - Prob. 54SRCh. 5.3 - Prob. 55SRCh. 5.3 - Prob. 56SRCh. 5.3 - Prob. 57SRCh. 5.3 - Prob. 58SRCh. 5.3 - Prob. 59SRCh. 5.3 - Prob. 60SRCh. 5.3 - Prob. 61SCh. 5.3 - Prob. 62SCh. 5.3 - Prob. 63SCh. 5.3 - Prob. 64SCh. 5.3 - Prob. 65SCh. 5.3 - Prob. 66SCh. 5.4 - Prob. 1AGPCh. 5.4 - Prob. 1BGPCh. 5.4 - Prob. 2AGPCh. 5.4 - Prob. 2BGPCh. 5.4 - Prob. 3GPCh. 5.4 - Prob. 4AGPCh. 5.4 - Prob. 4BGPCh. 5.4 - Prob. 1CYUCh. 5.4 - Prob. 2CYUCh. 5.4 - Prob. 3CYUCh. 5.4 - Prob. 4CYUCh. 5.4 - Prob. 5CYUCh. 5.4 - Prob. 6CYUCh. 5.4 - Prob. 7CYUCh. 5.4 - Prob. 8CYUCh. 5.4 - Prob. 9CYUCh. 5.4 - Prob. 10CYUCh. 5.4 - Prob. 11PPSCh. 5.4 - Prob. 12PPSCh. 5.4 - Prob. 13PPSCh. 5.4 - Prob. 14PPSCh. 5.4 - Prob. 15PPSCh. 5.4 - Prob. 16PPSCh. 5.4 - Prob. 17PPSCh. 5.4 - Prob. 18PPSCh. 5.4 - Prob. 19PPSCh. 5.4 - Prob. 20PPSCh. 5.4 - Prob. 21PPSCh. 5.4 - Prob. 22PPSCh. 5.4 - Prob. 23PPSCh. 5.4 - Prob. 24PPSCh. 5.4 - Prob. 25PPSCh. 5.4 - Prob. 26PPSCh. 5.4 - Prob. 27PPSCh. 5.4 - Prob. 28PPSCh. 5.4 - Prob. 29PPSCh. 5.4 - Prob. 30PPSCh. 5.4 - Prob. 31PPSCh. 5.4 - Prob. 32PPSCh. 5.4 - Prob. 33PPSCh. 5.4 - Prob. 34PPSCh. 5.4 - Prob. 35PPSCh. 5.4 - Prob. 36PPSCh. 5.4 - Prob. 37PPSCh. 5.4 - Prob. 38PPSCh. 5.4 - Prob. 39PPSCh. 5.4 - Prob. 40PPSCh. 5.4 - Prob. 41PPSCh. 5.4 - Prob. 42PPSCh. 5.4 - Prob. 43PPSCh. 5.4 - Prob. 44PPSCh. 5.4 - Prob. 45PPSCh. 5.4 - Prob. 46PPSCh. 5.4 - Prob. 47PPSCh. 5.4 - Prob. 48PPSCh. 5.4 - Prob. 49PPSCh. 5.4 - Prob. 50PPSCh. 5.4 - Prob. 51PPSCh. 5.4 - Prob. 52PPSCh. 5.4 - Prob. 53PPSCh. 5.4 - Prob. 54PPSCh. 5.4 - Prob. 55PPSCh. 5.4 - Prob. 56PPSCh. 5.4 - Prob. 57PPSCh. 5.4 - Prob. 58PPSCh. 5.4 - Prob. 59PPSCh. 5.4 - Prob. 60PPSCh. 5.4 - Prob. 61PPSCh. 5.4 - Prob. 62PPSCh. 5.4 - Prob. 63PPSCh. 5.4 - Prob. 64PPSCh. 5.4 - Prob. 65PPSCh. 5.4 - Prob. 66PPSCh. 5.4 - Prob. 67HPCh. 5.4 - Prob. 68HPCh. 5.4 - Prob. 69HPCh. 5.4 - Prob. 70HPCh. 5.4 - Prob. 71HPCh. 5.4 - Prob. 72HPCh. 5.4 - Prob. 73STPCh. 5.4 - Prob. 74STPCh. 5.4 - Prob. 75STPCh. 5.4 - Prob. 76STPCh. 5.4 - Prob. 77SRCh. 5.4 - Prob. 78SRCh. 5.4 - Prob. 79SRCh. 5.4 - Prob. 80SRCh. 5.4 - Prob. 81SRCh. 5.4 - Prob. 82SRCh. 5.4 - Prob. 83SRCh. 5.4 - Prob. 84SRCh. 5.4 - Prob. 85SRCh. 5.4 - Prob. 86SRCh. 5.4 - Prob. 87SCh. 5.4 - Prob. 88SCh. 5.4 - Prob. 89SCh. 5.4 - Prob. 90SCh. 5.4 - Prob. 91SCh. 5.4 - Prob. 92SCh. 5.5 - Prob. 1AGPCh. 5.5 - Prob. 1BGPCh. 5.5 - Prob. 2AGPCh. 5.5 - Prob. 2BGPCh. 5.5 - Prob. 3GPCh. 5.5 - Prob. 4AGPCh. 5.5 - Prob. 4BGPCh. 5.5 - Prob. 5AGPCh. 5.5 - Prob. 5BGPCh. 5.5 - Prob. 1CYUCh. 5.5 - Prob. 2CYUCh. 5.5 - Prob. 3CYUCh. 5.5 - Prob. 4CYUCh. 5.5 - Prob. 5CYUCh. 5.5 - Prob. 6CYUCh. 5.5 - Prob. 7CYUCh. 5.5 - Prob. 8CYUCh. 5.5 - Prob. 9CYUCh. 5.5 - Prob. 10CYUCh. 5.5 - Prob. 11CYUCh. 5.5 - Prob. 12CYUCh. 5.5 - Prob. 13CYUCh. 5.5 - Prob. 14CYUCh. 5.5 - Prob. 15CYUCh. 5.5 - Prob. 16CYUCh. 5.5 - Prob. 17CYUCh. 5.5 - Prob. 18PPSCh. 5.5 - Prob. 19PPSCh. 5.5 - Prob. 20PPSCh. 5.5 - Prob. 21PPSCh. 5.5 - Prob. 22PPSCh. 5.5 - Prob. 23PPSCh. 5.5 - Prob. 24PPSCh. 5.5 - Prob. 25PPSCh. 5.5 - Prob. 26PPSCh. 5.5 - Prob. 27PPSCh. 5.5 - Prob. 28PPSCh. 5.5 - Prob. 29PPSCh. 5.5 - Prob. 30PPSCh. 5.5 - Prob. 31PPSCh. 5.5 - Prob. 32PPSCh. 5.5 - Prob. 33PPSCh. 5.5 - Prob. 34PPSCh. 5.5 - Prob. 35PPSCh. 5.5 - Prob. 36PPSCh. 5.5 - Prob. 37PPSCh. 5.5 - Prob. 38PPSCh. 5.5 - Prob. 39PPSCh. 5.5 - Prob. 40PPSCh. 5.5 - Prob. 41PPSCh. 5.5 - Prob. 42PPSCh. 5.5 - Prob. 43PPSCh. 5.5 - Prob. 44PPSCh. 5.5 - Prob. 45PPSCh. 5.5 - Prob. 46PPSCh. 5.5 - Prob. 47PPSCh. 5.5 - Prob. 48PPSCh. 5.5 - Prob. 49PPSCh. 5.5 - Prob. 50PPSCh. 5.5 - Prob. 51HPCh. 5.5 - Prob. 52HPCh. 5.5 - Prob. 53HPCh. 5.5 - Prob. 54HPCh. 5.5 - Prob. 55HPCh. 5.5 - Prob. 56STPCh. 5.5 - Prob. 57STPCh. 5.5 - Prob. 58STPCh. 5.5 - Prob. 59STPCh. 5.5 - Prob. 60SRCh. 5.5 - Prob. 61SRCh. 5.5 - Prob. 62SRCh. 5.5 - Prob. 63SRCh. 5.5 - Prob. 64SRCh. 5.5 - Prob. 65SRCh. 5.5 - Prob. 66SRCh. 5.5 - Prob. 67SRCh. 5.5 - Prob. 68SRCh. 5.5 - Prob. 69SRCh. 5.5 - Prob. 70SRCh. 5.5 - Prob. 71SRCh. 5.5 - Prob. 72SRCh. 5.5 - Prob. 73SRCh. 5.5 - Prob. 74SRCh. 5.5 - Prob. 75SCh. 5.5 - Prob. 76SCh. 5.5 - Prob. 77SCh. 5.5 - Prob. 78SCh. 5 - Prob. 1QCCh. 5 - Prob. 2QCCh. 5 - Prob. 3QCCh. 5 - Prob. 4QCCh. 5 - Prob. 5QCCh. 5 - Prob. 6QCCh. 5 - Prob. 7QCCh. 5 - Prob. 8QCCh. 5 - Prob. 9QCCh. 5 - Prob. 10QCCh. 5 - Prob. 11QCCh. 5 - Prob. 12QCCh. 5 - Prob. 13QCCh. 5 - Prob. 14QCCh. 5 - Prob. 15QCCh. 5 - Prob. 16QCCh. 5 - Prob. 17QCCh. 5 - Prob. 18QCCh. 5 - Prob. 19QCCh. 5 - Prob. 20QCCh. 5 - Prob. 21QCCh. 5 - Prob. 1MCQCh. 5 - Prob. 2MCQCh. 5 - Prob. 3MCQCh. 5 - Prob. 4MCQCh. 5 - Prob. 5MCQCh. 5 - Prob. 6MCQCh. 5 - Prob. 7MCQCh. 5 - Prob. 8MCQCh. 5 - Prob. 9MCQCh. 5 - Prob. 10MCQCh. 5 - Prob. 11MCQCh. 5 - Prob. 12MCQCh. 5 - Prob. 13MCQCh. 5 - Prob. 14MCQCh. 5 - Prob. 15MCQCh. 5 - Prob. 16MCQCh. 5 - Prob. 17MCQCh. 5 - Prob. 18MCQCh. 5 - Prob. 19MCQCh. 5 - Prob. 20MCQCh. 5 - Prob. 1SGRCh. 5 - Prob. 2SGRCh. 5 - Prob. 3SGRCh. 5 - Prob. 4SGRCh. 5 - Prob. 5SGRCh. 5 - Prob. 6SGRCh. 5 - Prob. 7SGRCh. 5 - Prob. 8SGRCh. 5 - Prob. 9SGRCh. 5 - Prob. 10SGRCh. 5 - Prob. 11SGRCh. 5 - Prob. 12SGRCh. 5 - Prob. 13SGRCh. 5 - Prob. 14SGRCh. 5 - Prob. 15SGRCh. 5 - Prob. 16SGRCh. 5 - Prob. 17SGRCh. 5 - Prob. 18SGRCh. 5 - Prob. 19SGRCh. 5 - Prob. 20SGRCh. 5 - Prob. 21SGRCh. 5 - Prob. 22SGRCh. 5 - Prob. 23SGRCh. 5 - Prob. 24SGRCh. 5 - Prob. 25SGRCh. 5 - Prob. 26SGRCh. 5 - Prob. 27SGRCh. 5 - Prob. 28SGRCh. 5 - Prob. 29SGRCh. 5 - Prob. 30SGRCh. 5 - Prob. 31SGRCh. 5 - Prob. 32SGRCh. 5 - Prob. 33SGRCh. 5 - Prob. 34SGRCh. 5 - Prob. 35SGRCh. 5 - Prob. 36SGRCh. 5 - Prob. 37SGRCh. 5 - Prob. 38SGRCh. 5 - Prob. 39SGRCh. 5 - Prob. 40SGRCh. 5 - Prob. 41SGRCh. 5 - Prob. 42SGRCh. 5 - Prob. 43SGRCh. 5 - Prob. 44SGRCh. 5 - Prob. 45SGRCh. 5 - Prob. 46SGRCh. 5 - Prob. 47SGRCh. 5 - Prob. 48SGRCh. 5 - Prob. 1PTCh. 5 - Prob. 2PTCh. 5 - Prob. 3PTCh. 5 - Prob. 4PTCh. 5 - Prob. 5PTCh. 5 - Prob. 6PTCh. 5 - Prob. 7PTCh. 5 - Prob. 8PTCh. 5 - Prob. 9PTCh. 5 - Prob. 10PTCh. 5 - Prob. 11PTCh. 5 - Prob. 12PTCh. 5 - Prob. 13PTCh. 5 - Prob. 14PTCh. 5 - Prob. 15PTCh. 5 - Prob. 16PTCh. 5 - Prob. 17PTCh. 5 - Prob. 18PTCh. 5 - Prob. 19PTCh. 5 - Prob. 20PTCh. 5 - Prob. 21PTCh. 5 - Prob. 22PTCh. 5 - Prob. 23PTCh. 5 - Prob. 24PTCh. 5 - Prob. 25PTCh. 5 - Prob. 1ECh. 5 - Prob. 2ECh. 5 - Prob. 3ECh. 5 - Prob. 1STPCh. 5 - Prob. 2STPCh. 5 - Prob. 3STPCh. 5 - Prob. 4STPCh. 5 - Prob. 5STPCh. 5 - Prob. 6STPCh. 5 - Prob. 7STPCh. 5 - Prob. 8STPCh. 5 - Prob. 9STPCh. 5 - Prob. 10STPCh. 5 - Prob. 11STPCh. 5 - Prob. 12STPCh. 5 - Prob. 13STPCh. 5 - Prob. 14STP

Additional Math Textbook Solutions

Find more solutions based on key concepts
In each of Exercises 21–30, draw a linear graph to represent the given information. Be sure to label and number...

Elementary Algebra: Concepts and Applications (10th Edition)

OTHER TYPES OF EQUATIONS For the following exercises, solve the equations. 3x7=5

College Algebra

Fill in each blank so that the resulting statement is true. 1. A combination of numbers, variables, and opera...

College Algebra (7th Edition)

For items a-m, decide if the given statement is true or false, and give a brief justification for your answer. ...

Differential Equations and Linear Algebra (4th Edition)

44. Retirement Hennie and Bob inherit $100,000 and plan to invest part of it for 25 years at 10%, compounded mo...

College Algebra in Context with Applications for the Managerial, Life, and Social Sciences (5th Edition)

A linear equation is solved by using the intersection of graphs method. Find the solution by interpreting the g...

College Algebra with Modeling & Visualization (6th Edition)

Knowledge Booster
Background pattern image
Algebra
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Text book image
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:PEARSON
Text book image
Contemporary Abstract Algebra
Algebra
ISBN:9781305657960
Author:Joseph Gallian
Publisher:Cengage Learning
Text book image
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Text book image
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:9780135163078
Author:Michael Sullivan
Publisher:PEARSON
Text book image
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:9780980232776
Author:Gilbert Strang
Publisher:Wellesley-Cambridge Press
Text book image
College Algebra (Collegiate Math)
Algebra
ISBN:9780077836344
Author:Julie Miller, Donna Gerken
Publisher:McGraw-Hill Education
SEE MORE TEXTBOOKS
What is a Linear Equation in One Variable?; Author: Don't Memorise;https://www.youtube.com/watch?v=lDOYdBgtnjY;License: Standard YouTube License, CC-BY
Linear Equation | Solving Linear Equations | What is Linear Equation in one variable ?; Author: Najam Academy;https://www.youtube.com/watch?v=tHm3X_Ta_iE;License: Standard YouTube License, CC-BY