Isolating a Variable

When you have actually an equation through one variable and also you require to know the value of that variable, your task is to isolation the variable x. It’s called “isolating” because at the finish of the process the change is alone on one next of the equation (and we deserve to see what it equals).

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The basic method to isolate a variable is to “do something come both sides” that the equation, such as add, subtract, multiply, or division both political parties of the equation by the same number. By repeating this process, us can acquire the variable isolated top top one side of the equation. The trick is to know which to work to execute in i beg your pardon order.

For example, if we start with the equation to solve:


We subtract 4 native both sides:


Then we integrate terms come get:


Finally, we division by the coefficient of x:



When you’re provided more difficult equations, the sure means to isolate a change is to carry out the complying with steps:

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

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

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

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

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

At five steps, this process might seem laborious. If girlfriend remember to eliminate fractions very first and divide last, that’s a good start. For this reason and since isolating is a typical procedure ~ above the GMAT, a good way to practice is to dive right into some reality questions.

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Practice Questions

Variable in a Denominator:

Needless Variable:

Linear Equations v Fractions:

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