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- 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
Discuss the differences between taste and flavor, including how other sensory inputs contribute to our perception of flavor.
taste refers to your understanding of the flavor . while flavor one The other hand is refers to sort of just a blend things.
Faith
While taste primarily relies on our taste buds, flavor involves a complex interplay between taste and aroma
Kamara
which drugs can we use for ulcers
Omeprazole
Cimetidine / Tagament
For the complicated once ulcer - kit
Patrick
what is the function of lymphatic system
to drain extracellular fluid all over the body.
asegid
The lymphatic system plays several crucial roles in the human body, functioning as a key component of the immune system and contributing to the maintenance of fluid balance. Its main functions include:
1. Immune Response: The lymphatic system produces and transports lymphocytes, which are a type of
asegid
to transport fluids fats proteins and lymphocytes to the blood stream as lymph
Adama
Anatomy is the identification and description of the structures of living things
Kamara
what's the difference between anatomy and physiology
Anatomy is the study of the structure of the body, while physiology is the study of the function of the body. Anatomy looks at the body's organs and systems, while physiology looks at how those organs and systems work together to keep the body functioning.
AI-Robot
what is enzymes all about?
Enzymes are proteins that help speed up chemical reactions in our bodies. Enzymes are essential for digestion, liver function and much more. Too much or too little of a certain enzyme can cause health problems
Kamara
how does the stomach protect itself from the damaging effects of HCl
little girl okay how does the stomach protect itself from the damaging effect of HCL
Wulku
it is because of the enzyme that the stomach produce that help the stomach from the damaging effect of HCL
Kamara
function of digestive system
function of digestive
Ali
what is the normal body temperature
please why 37 degree selcius normal temperature
Mark
the normal temperature is 37°c or 98.6 °Fahrenheit is important for maintaining the homeostasis in the body
the body regular this temperature through the process called thermoregulation which involves brain skin muscle and other organ working together to maintain stable internal temperature
Stephanie
anaemia is the decrease in RBC count hemoglobin count and PVC count
Eniola
what is the pH of the vagina
how does Lysin attack pathogens
Diya
I information on anatomy position and digestive system and there enzyme
anatomy of the female external genitalia
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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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