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- Elementary algebra
- Solving linear equations and
- Summary of key concepts
This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr.
In this chapter, the emphasis is on the mechanics of equation solving, which clearly explains how to isolate a variable. The goal is to help the student feel more comfortable with solving applied problems. Ample opportunity is provided for the student to practice translating words to symbols, which is an important part of the "Five-Step Method" of solving applied problems (discussed in modules (<link document="m21980"/>) and (<link document="m21979"/>)).
This module provides a summary of the key concepts of the chapter "Solving Linear Equations and Inequalities".
Summary of key concepts
Identity (
[link] )
An equation that is true for all acceptable values of the variable is called
identity .
is an identity.
Contradiction (
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Contradictions are equations that are never true regardless of the value substituted for the variable.
is a contradiction.
Conditional equation (
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An equation whose truth is conditional upon the value selected for the variable is called a
conditional equation .
Solutions and solving an equation (
[link] )
The collection of values that make an equation true are called the
solutions of the equation. An equation is said to be
solved when all its solutions have been found.
Equivalent equations (
[link] ,
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Equations that have precisely the same collection of solutions are called
equivalent equations .
An equivalent equation can be obtained from a particular equation by applying the
same binary operation to
both sides of the equation, that is,
- adding or subtracting the
same number to or from
both sides of that particular equation.
- multiplying or dividing
both sides of that particular equation by the
same non-zero number.
Literal equation (
[link] )
A
literal equation is an equation that is composed of more than one variable.
Recognizing an identity (
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If, when solving an equation, all the variables are eliminated and a true statement results, the equation is an
identity .
Recognizing a contradiction (
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If, when solving an equation, all the variables are eliminated and a false statement results, the equation is a
contradiction .
Translating from verbal to mathematical expressions (
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When solving word problems it is absolutely necessary to know how certain words translate into mathematical symbols.
Five-step method for solving word problems (
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- Let
(or some other letter) represent the unknown quantity.
- Translate the words to mathematics and form an equation. A diagram may be helpful.
- Solve the equation.
- Check the solution by substituting the result into the original statement of the problem.
- Write a conclusion.
Linear inequality (
[link] )
A
linear inequality is a mathematical statement that one linear expression is greater than or less than another linear expression.
Inequality notation (
[link] )
Compound inequality (
[link] )
An inequality of the form
is called a
compound inequality .
Solution to an equation in two variables and ordered pairs (
[link] )
A pair of values that when substituted into an equation in two variables produces a true statement is called a solution to the equation in two variables. These values are commonly written as an
ordered pair . The expression
is an ordered pair. In an ordered pair, the independent variable is written first and the dependent variable is written second.
Questions & Answers
Three charges q_{1}=+3\mu C, q_{2}=+6\mu C and q_{3}=+8\mu C are located at (2,0)m (0,0)m and (0,3) coordinates respectively. Find the magnitude and direction acted upon q_{2} by the two other charges.Draw the correct graphical illustration of the problem above showing the direction of all forces.
To solve this problem, we need to first find the net force acting on charge q_{2}. The magnitude of the force exerted by q_{1} on q_{2} is given by F=\frac{kq_{1}q_{2}}{r^{2}} where k is the Coulomb constant, q_{1} and q_{2} are the charges of the particles, and r is the distance between them.
Muhammed
What is the direction and net electric force on q_{1}= 5µC located at (0,4)r due to charges q_{2}=7mu located at (0,0)m and q_{3}=3\mu C located at (4,0)m?
what is the change in momentum of a body?
Capacitor is a separation of opposite charges using an insulator of very small dimension between them. Capacitor is used for allowing an AC (alternating current) to pass while a DC (direct current) is blocked.
Gautam
A motor travelling at 72km/m on sighting a stop sign applying the breaks such that under constant deaccelerate in the meters of 50 metres what is the magnitude of the accelerate
What is Thermodynamics
Muordit
velocity can be 72 km/h in question. 72 km/h=20 m/s, v^2=2.a.x , 20^2=2.a.50, a=4 m/s^2.
Mehmet
A boat travels due east at a speed of 40meter per seconds across a river flowing due south at 30meter per seconds. what is the resultant speed of the boat
50 m/s due south east
Someone
which has a higher temperature, 1cup of boiling water or 1teapot of boiling water which can transfer more heat 1cup of boiling water or 1 teapot of boiling water explain your . answer
I believe temperature being an intensive property does not change for any amount of boiling water whereas heat being an extensive property changes with amount/size of the system.
Someone
temperature for any amount of water to boil at ntp is 100⁰C (it is a state function and and intensive property) and it depends both will give same amount of heat because the surface available for heat transfer is greater in case of the kettle as well as the heat stored in it but if you talk.....
Someone
about the amount of heat stored in the system then in that case since the mass of water in the kettle is greater so more energy is required to raise the temperature b/c more molecules of water are present in the kettle
Someone
physics, biology and chemistry
this is my Field
ALIYU
field is a region of space under the influence of some physical properties
Collete
what is ogarnic chemistry
determine the slope giving that 3y+ 2x-14=0
WISDOM
Another formula for Acceleration
pratica A on solution of hydro chloric acid,B is a solution containing 0.5000 mole ofsodium chlorid per dm³,put A in the burret and titrate 20.00 or 25.00cm³ portion of B using melting orange as the indicator. record the deside of your burret tabulate the burret reading and calculate the average volume of acid used?
how do lnternal energy measures
Esrael
Two bodies attract each other electrically. Do they both have to be charged? Answer the same question if the bodies repel one another.
No. According to Isac Newtons law. this two bodies maybe you and the wall beside you.
Attracting depends on the mass och each body and distance between them.
Dlovan
Are you really asking if two bodies have to be charged to be influenced by Coulombs Law?
Robert
like charges repel while unlike charges atttact
Raymond
What is specific heat capacity
Specific heat capacity is a measure of the amount of energy required to raise the temperature of a substance by one degree Celsius (or Kelvin). It is measured in Joules per kilogram per degree Celsius (J/kg°C).
AI-Robot
specific heat capacity is the amount of energy needed to raise the temperature of a substance by one degree Celsius or kelvin
ROKEEB
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Source:
OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
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