Finding the Unknown

Overview

Finding the Unknown introduces simple equations. We learn to form equations from word problems and solve them to find the value of an unknown letter.

Key concepts

• An equation says two expressions are equal.
• The unknown (variable) is the value we want to find.
• Balance method: do the same operation to both sides.
• Inverse operations undo each other (+ and −, × and ÷).

Important formulae

• If x + a = b, then x = b − a
• If x − a = b, then x = b + a
• If ax = b, then x = b ÷ a

Solved example

1. Solve 2x + 3 = 11.
2. Subtract 3 from both sides: 2x = 8.
3. Divide both sides by 2: x = 4.

Important questions

1. Solve x + 7 = 12.
2. Solve 5x = 35.
3. Solve x/3 = 6.
4. Three more than twice a number is 15. Find the number.

Quick revision

Keep the equation balanced by doing the same step on both sides, and use inverse operations to isolate the variable. Always check by substituting your answer back.