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In a mathematical equation, the expressions on either or both sides of the equality sign (=) may involve one or more symbols standing for unknown quantities: the "variables." A standard method of solving an equation is by transforming it into another that has the same set of solutions. When all occurrences of a variable appear on just one side of the equality, that variable has been "isolated." Some people might apply a stricter criterion in which one side of the equation must consist only of that variable.
For example, in the equation
x + 3 = 2x + 1
there is one variable "x" but it is not isolated. It can be isolated by subtracting x+1 from both sides to produce the equivalent equation
(x + 3) - (x + 1) = (2x + 1) - (x + 1)
Rules of arithmetic permit the left hand side to be rewritten as "2" and the right hand side to be rewritten as "x", giving
2 = x.
Now x is an isolated variable.
See the Wikipedia article on "Elementary algebra" for details.
The term "isolated variable" is also used in statistics in many slightly different ways. It appears to be used by investigators to refer to an experiment in which exactly one of many factors under experimental control is varied to determine its effect on the experimental outcome. This factor is called the "isolated variable."
Another related meaning is in a multiple regression context where, as part of the analysis, all but one of the explanatory variables is left out: the remaining one is the "isolated variable." See Walter et al., "Creatinine clearance versus serum creatinine as a risk factor in cardiac surgery," BMC Surgery 2003, 3:4 at http://www.biomedcentral.com/1471-2482/3/4 for an example.
Yet another related meaning is that a statistical variable 'X' is "isolated" when there is no direct causal relationship between 'X' and any of the other variables in the statistical model. For an example of this usage, see the "final review questions" page for the "Quantitative Research in Public Administration" course at NC State University at http://www2.chass.ncsu.edu/garson/PA765/ch15qanda.htm.
What else can I help you with?
When an equation contains addition can the variable be isolated by performing the opposite process namely subtraction?
Yes.
Was of finding the value of the variable?
Finding the value of a variable involves solving an equation or a set of equations where the variable is present. This process typically includes isolating the variable on one side of the equation through various algebraic techniques, such as addition, subtraction, multiplication, and division. Once the variable is isolated, its value can be determined based on the given information. This is a fundamental concept in algebra and critical for solving mathematical problems.
What is the value of the variable that makes equations true?
The value of the variable that makes an equation true is known as the solution to the equation. It is the number that, when substituted for the variable, satisfies the equation's conditions. To find this value, one typically manipulates the equation using algebraic techniques until the variable is isolated on one side. The resulting value can then be verified by substituting it back into the original equation.
How do we solve- equations with the variable on both sides of the equal sign?
To solve equations with variables on both sides, first isolate the variable by moving all terms involving the variable to one side of the equation and constant terms to the other side. This can be done by adding or subtracting terms as necessary. Once the variable is isolated, simplify the equation if needed and solve for the variable. Finally, check your solution by substituting it back into the original equation.
How do you isolate a variable?
To isolate a variable, you need to manipulate the equation so that the variable is on one side by itself. This typically involves performing inverse operations, such as adding, subtracting, multiplying, or dividing both sides of the equation by the same value. It's important to apply these operations consistently to maintain the equality. Once the variable is isolated, you can clearly see its value in relation to the other terms in the equation.
What is the definition of isolate the variable?
In algebra, its to move the pieces of the equation around so that the variable is isolated to only one side of the sign
When an equation contains addition can the variable be isolated by performing the opposite process namely subtraction?
Yes.
How many variable should be tested and isolated in a good experiment?
One. If there is only one variable being tested, when you compare it to the control, you know that was the cause of a change.
What is dependent quantity means in math?
A variable that depends on one or more other variables. For equations such as y = 3x - 2, the dependent variable is y. The value of y depends on the value chosen for x. Usually the dependent variable is isolated on one side of an equation. Formally, a dependent variable is a variable in an expression, equation, orfunction that has its value determined by the choice of value(s) of other variable(s).
Why are variables isolated?
Variables are isolated in order to prevent interference or contamination from other factors. By isolating variables, researchers can accurately determine the effect of the specific variable being studied. This helps ensure the validity and reliability of the results obtained from an experiment.
7 ex equals 27.09?
the question is: 7x = 27.09so what you do is divide 27.09 by 7 to get x the variable alone, or isolated. making the answerx= 3.87
Was of finding the value of the variable?
Finding the value of a variable involves solving an equation or a set of equations where the variable is present. This process typically includes isolating the variable on one side of the equation through various algebraic techniques, such as addition, subtraction, multiplication, and division. Once the variable is isolated, its value can be determined based on the given information. This is a fundamental concept in algebra and critical for solving mathematical problems.
What is the value of the variable that makes equations true?
The value of the variable that makes an equation true is known as the solution to the equation. It is the number that, when substituted for the variable, satisfies the equation's conditions. To find this value, one typically manipulates the equation using algebraic techniques until the variable is isolated on one side. The resulting value can then be verified by substituting it back into the original equation.
True or false. the control subject of an experiment be exposed to all variables?
False. The control subject (Or control group) should be kept isolated from the variables of the experiment. This group will detemine if changing a variable is better or worse than not changing the variable.
How do we solve- equations with the variable on both sides of the equal sign?
To solve equations with variables on both sides, first isolate the variable by moving all terms involving the variable to one side of the equation and constant terms to the other side. This can be done by adding or subtracting terms as necessary. Once the variable is isolated, simplify the equation if needed and solve for the variable. Finally, check your solution by substituting it back into the original equation.
How do you isolate a variable?
To isolate a variable, you need to manipulate the equation so that the variable is on one side by itself. This typically involves performing inverse operations, such as adding, subtracting, multiplying, or dividing both sides of the equation by the same value. It's important to apply these operations consistently to maintain the equality. Once the variable is isolated, you can clearly see its value in relation to the other terms in the equation.
When is an experimental variable good?
A experimental variable is good when you are trying to test an experiment. A variable may be easily controlled, isolated, and measured. For instance a difficult experimental variable may be a persons gender. You can control if a man or woman participates in your experiment, you may even easily identify which gender they are. But it may be difficult to determine if the results are due to inherent genetic differences, or social influence on their lives. that isn't to say it can't be used, it just is more complicated than a "good" variable. A good variable could be something like Height, eye color, etc. that don't have that confounding aspect. In summary - The primary variable should be controllable, where you can directly manipulate it. The more controllable, the better. The variable you measure, and the one you control, should be isolated. You should be able to distinguish it from other complicating factors. The variable should be measurable. Some things are easy, such as height. Others not so easy, such as pain, or opinion. Developing tools to measure such variables are key.
