Solving One-Variable Equations

Definition

A one-variable equation is a math sentence with an equals sign and one unknown number, called a variable (usually a letter like x or n). Solving it means finding the value of that variable that makes the equation true. You do this by undoing whatever is being done to the variable, keeping both sides of the equals sign balanced the whole time.

Key words

Variable

A letter (like x, y, or n) that stands for an unknown number you are trying to find.

Equation

A math sentence with an equals sign showing that two expressions have the same value.

Solution

The number that replaces the variable and makes the equation true.

Inverse Operation

The opposite math operation used to undo something — addition undoes subtraction, multiplication undoes division.

Isolate

To get the variable all by itself on one side of the equals sign.

Coefficient

The number multiplied by the variable, like the 3 in 3x.

Constant

A plain number in an equation with no variable attached, like the 5 in x + 5 = 12.

Balance

Whatever you do to one side of the equation, you must do the exact same thing to the other side.

Worked examples

Common mistakes

• Doing the operation to only one side — you must always do the same thing to BOTH sides.
• Subtracting when you should add (or vice versa) — always use the opposite operation to undo.
• Forgetting to handle a coefficient: in 3x = 12, students sometimes just subtract 3 instead of dividing both sides by 3.
• Stopping too early — leaving the answer as 2x = 8 instead of finishing the last step to get x = 4.
• Sign errors — especially when negatives are involved, like thinking x - 5 = 10 gives x = 5 instead of x = 15.

FAQs