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A single equation with two variables can be solved for one of the variables, in terms of the other. For example, a rectangle's area is A = wh (width x height). Now let's assume you know the area: 20 = wh. You can solve for any of these variables in terms of the other, for example, w = 20/h. That is, once you assign a value to "h", you can calculate "w". But you don't know the specific values for "w" and "h", because the equation has an infinite number of solutions.
If you want to know specific values for the variables, in general, you need two different equations with 2 variables - or 3 equations with 3 variables, etc.
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Solve the equation for two less than four times the number is equal to two more than three times the same number?
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What is the property that you can subtract the same number from both sides of an equation the new equation will have the same solution?
The property is: If equals are subtracted from equals, the results are equal.
Why is it important to keep both sides of the equation equal?
If both sides of an equation are not equal, it won't be an equation any more! In solving equations, the strategy is to change both sides in the same way, so that an 'equivalent' equation is produced. An equivalent equation has the same solution as the original equation. You are aiming for an equation in which the variable is alone on one side. The quantity on the other side is the solution.
When solving an equation why is it necessary to perform the same operation on each side of the equals sign?
If two things are equal (as implied by the equals sign), then if you do something to one of those things (one side of the equal sign), unless you do the same to the other thing (the other side of the equals sign), then the two things will no longer be equal. Thus when solving, if you do not so the same to both sides, the sides will no longer be equal to each other and you will not solve the problem correctly.
How can you solve an equation to get an equivalent equation?
In general, if you apply the same operation to both sides of an equation, you get an equivalent equation - at least if you do simple things like adding, subtracting, multiplying by a non-zero number, and dividing by some number.
