Finding the Unknown

An equation is a balance. Do the same thing to both sides to find the unknown, and turn word problems into equations.

Key ideas

• An equation says two expressions are equal; solving it means finding the value that makes it true.
• Keep the balance: add, subtract, multiply or divide both sides by the same number.
• Undo the operations in reverse order: first the adding or subtracting, then the multiplying or dividing.
• Check the answer by putting it back into the original equation.
• For a word problem, choose a letter for the unknown, write the equation from the facts, solve it, and answer in words.

Remember

Watch out

• Doing an operation to one side only.
• Dividing before subtracting, as in 4b + 10 = 66 → b + 10 = 16.5.
• Stopping at the value of the letter without answering the question (for example, giving the breadth when the length was asked).

Worked example