The answer depends on the nature of the equation. Some equations can be solved by analytical methods. For example, you can carry out the basic operations of arithmetic on both sides of the equation so as to isolate the variable. Isolating the variable means that only the variable appears on one side of the equation and the other side contains only arithmetic expressions which can be evaluated.
For example, if the equation is 3x + 5 = 7
then subtracting 5 from both sides gives 3x = 2
and dividing both sides by 3 gives x = 2/3.
Some equations cannot be solved in this way. Sometimes there are formulae - such as the quadratic formula - while at other times the only option is to use numerical methods (trial and improvement or its more sophisticated versions).
Depending on the type of equation, this can be very simple or very complicated. The basic procedure is shown, with many example, in any high school algebra textbook. The main idea (for the simpler cases) is to do the same operation on both sides of the equation, until the variable is alone on one side. Here is an example:2x + 5 = 25
The objective is to have the "x" alone. One way of going in this direction is to subtract 5 from both sides, to get rid of the 5:
2x + 5 - 5 = 25 - 5
or:
2x = 20
Next, you need to get rid of the 2 (your objective is still to have the "x" alone on the left):
2x/2 = 20/2
or: (2/2)x = 10
or: x = 10
substitution
No. The goal is to find a value of the variable(s) for which the solution is true. Getting the variable by itself is only a part of the process, not the goal.
In a nonlinear equation, each variable must only have one solution.
Solution
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substitution
Substitution
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That's the "solution" of the equation.
a solution
That's the "solution" to the equation described by the sentence.
Isolating a single variable in terms of the rest of the equation provides a solution to that variable. That is, if you know the equation that equals the variable, then you can figure out its value.
No. The goal is to find a value of the variable(s) for which the solution is true. Getting the variable by itself is only a part of the process, not the goal.
For a value to be a solution to an equation, when you substitute the value for the variable, the equation becomes true. 4+B=6 B is the variable. 2 is the solution Substitute 2 for B 4+2=6 The equation is true.
In a nonlinear equation, each variable must only have one solution.
y = -2.5 is a equation. And solution to the equation is finding the value of the variable. If we see the equation y is already equal to -2.5 which is the solution to the equation.