GMAT Quantitative Review

3.0 Math Review

3.2 Algebra

3. Solving Linear Equations with One Unknown

To solve a linear equation with one unknown (that is, to find the value of the unknown that satisfies the equation), the unknown should be isolated on one side of the equation. This can be done by performing the same mathematical operations on both sides of the equation. Remember that if the same number is added to or subtracted from both sides of the equation, this does not change the equality; likewise, multiplying or dividing both sides by the same nonzero number does not change the equality. For example, to solve the equation image for x, the variable x can be isolated using the following steps:

image

The solution, image, can be checked by substituting it for x in the original equation to determine whether it satisfies that equation:

image

Therefore, image is the solution.