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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
A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
what are the types of wave
Maurice
fine, how about you?
Mohammed
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
Who can show me the full solution in this problem?
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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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