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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 (
[link] )
Contradictions are equations that are never true regardless of the value substituted for the variable.
is a contradiction.
Conditional equation (
[link] )
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] ,
[link] )
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 (
[link] )
If, when solving an equation, all the variables are eliminated and a true statement results, the equation is an
identity .
Recognizing a contradiction (
[link] )
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 (
[link] )
When solving word problems it is absolutely necessary to know how certain words translate into mathematical symbols.
Five-step method for solving word problems (
[link] )
- 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
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How can I develope my cognitive domain
why is communication effective
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
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Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
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Wekolamo
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ARC
A child is a member of community not society elucidate ?
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compare and contrast skinner's perspective on personality development on freud
Skinner skipped the whole unconscious phenomenon and rather emphasized on classical conditioning
war
explain how nature and nurture affect the development and later the productivity of an individual.
nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
Samuel
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Jonathan
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interpersonal relationships
What would be the best educational aid(s) for gifted kids/savants?
treat them normal, if they want help then give them.
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Saurabh
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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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