Isolating a Variable

When you have actually an equation v one variable and also you require to know the worth of that variable, your job is to isolate the variable x. It’s called “isolating” due to the fact that at the finish of the procedure the change is alone ~ above one next of the equation (and we deserve to see what it equals).

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The basic technique to isolate a variable is to “do something to both sides” that the equation, such as add, subtract, multiply, or division both sides of the equation by the same number. By repeating this process, we can get the variable isolated top top one next of the equation. The trick is to know which work to do in i m sorry order.

For example, if we begin with the equation come solve:


We subtract 4 from both sides:


Then we integrate terms to get:


Finally, we divide by the coefficient the x:



When you’re provided more an overwhelming equations, the sure method to isolate a change is to carry out the adhering to steps:

1. Eliminate any fractions present by multiplying both political parties by any denominators present.

2. Acquire all terms v the variable on the left side of the equation, and also all state without the change on the various other side.

3. Combine the terms on the left side, if possible.

4. Factor out the change on the left side, if necessary.

5. Divide both sides by the coefficient that the variable, leaving the variable isolated.

At five steps, this procedure might seem laborious. If girlfriend remember to get rid of fractions first and division last, that’s a good start. For this reason and since isolating is a typical procedure top top the GMAT, a an excellent way to exercise is come dive right into some reality questions.

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Practice Questions

Variable in a Denominator:

Needless Variable:

Linear Equations through Fractions:

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