# TASC Math Exam—Isolating a Variable

Not all equations that you’ll deal with on the TASC Math exam will be in single variables. There are common formulas that you may need to rearrange to find a certain variable or combination of variables.

The following examples illustrate how to isolate a particular variable given an equation or formula.

**Example 1:**

In this example, the formula is how force is calculated: Force equals mass times acceleration. As indicated, you’re solving for mass, *m*.

*F* = *ma*

To isolate *m*, notice that it’s being multiplied by *a*. This means you must divide by *a* on both sides.

**Example 2: **

This formula is used to calculate the volume of a cone given its height and radius. As indicated, you’re solving for the radius, *r*.

First, multiply by 3 to “get rid of” the fraction.

Don’t be scared of pi; it’s just a number that can be divided.

Lastly, take the square root of both sides to isolate *r*.

**Example 3:**

Because you’re looking for *xy*, you need to simplify both sides and get any terms with *xy* onto the same side.

Distribute 4*x*.

Notice that *xy* is on one side, and all that’s left is to divide by 2.

This means that the solution to this problem is 4 – 10*x*.