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- Elementary algebra
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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
Ayele, K., 2003. Introductory Economics, 3rd ed., Addis Ababa.
can you send the book attached ?
Ariel
the study of how humans make choices under conditions of scarcity
AI-Robot
U(x,y) = (x×y)1/2
find mu of x for y
U(x,y) = (xÃy)1/2
find mu of x for y
Desalegn
this is the study of how the society manages it's scarce resources
Belonwu
macroeconomic is the branch of economics which studies actions, scale, activities and behaviour of the aggregate economy as a whole.
husaini
difference between firm and industry
what's the difference between a firm and an industry
Abdul
firm is the unit which transform inputs to output where as industry contain combination of firms with similar production 😅😅
Abdulraufu
Suppose the demand function that a firm faces shifted from
Qd 120 3P
to
Qd 90 3P
and the supply function has shifted from
QS
20 2P
to
QS
10 2P .
a) Find the effect of this change on price and quantity.
b) Which of the changes in demand and supply is higher?
explain standard reason why economic is a science
factors influencing supply
scares
means__________________ends
resources. unlimited
Jan
economics is a science that studies human behaviour as a relationship b/w ends and scares means which have alternative uses
Jan
calculate the profit maximizing for demand and supply
Why qualify 28 supplies
Milan
out-of-pocket costs for a firm, for example, payments for wages and salaries, rent, or materials
AI-Robot
concepts of supply in microeconomics
identify a demand and a supply curve
there's a difference
Aryan
Demand curve shows that how supply and others conditions affect on demand of a particular thing and what percent demand increase whith increase of supply of goods
Israr
Hi Sir please how do u calculate Cross elastic demand and income elastic demand?
Abari
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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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