Isolating a Variable

When you have actually an equation with one variable and also you require to understand the worth of that variable, your task is to isolation the variable x. It’s dubbed “isolating” because at the end of the procedure the change is alone ~ above one next of the equation (and we have the right to see what the equals).

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The basic an approach to isolate a change is come “do something come both sides” the the equation, such together add, subtract, multiply, or divide both political parties of the equation by the very same number. By repeating this process, we can get the variable isolated top top one next of the equation. The cheat is to understand which work to execute in i beg your pardon order.

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


We subtract 4 indigenous both sides:


Then we combine terms come get:


Finally, we divide by the coefficient of x:



When you’re given more daunting equations, the sure way to isolation a variable 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. Get all terms v the change on the left side of the equation, and all state without the change on the other side.

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

4. Factor out the variable 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 it seems ~ laborious. If girlfriend remember to remove fractions first and division last, that’s a great start. For this reason and also since isolating is a common procedure top top the GMAT, a great way to practice is to dive right into some realistic questions.

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Practice Questions

Variable in a Denominator:

Needless Variable:

Linear Equations v Fractions:

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