By Matt McGew, updated August 30, 2022

Algebra introduces variables—symbols that stand in for numbers. In most problems, the letter “X” represents an unknown quantity. Solving for X means rearranging the equation so that X appears alone on one side. To do this, you rely on the fundamental rules of algebraic manipulation.

Step 1: Move constants to the opposite side

When X is added to a number, subtract that number from both sides. For example, in x + 5 = 12, rewrite it as x = 12 – 5 and obtain x = 7.

Step 2: Eliminate negative signs

If X is subtracted by a number, add that number to both sides. For example, x – 5 = 12 becomes x = 12 + 5, giving x = 17.

Step 3: Divide by a coefficient

When X is multiplied by a number, divide both sides by that number. For instance, 12x = 24 transforms to x = 24 / 12, resulting in x = 2.

Step 4: Multiply by a reciprocal

If X is divided by a number, multiply both sides by the same number to isolate X. For example, x / 2 = 3 becomes x = 2 × 3, yielding x = 6.