Chapter 4:Algebra, 4.5:Problems Involving the Change of Subject and Algebraic Equations

Changing the subject of a formula

• The subject is the variable that is alone on one side of the equation.

• To change the subject, rearrange the formula so the required variable is alone.

• Use inverse operations to undo operations.

Inverse operations

• Addition ↔ subtraction

• Multiplication ↔ division

• Squaring ↔ square root

• Cubing ↔ cube root

Basic method

• Identify the variable you want to make the subject.

• Undo operations in the correct order.

• Whatever you do to one side, do to the other side.

• Check that the new subject is completely isolated.

Equations with fractions

• Multiply both sides by the denominator to remove fractions.

• Then rearrange and simplify.

Equations with brackets

• Expand the brackets first if necessary.

• Collect like terms.

• Use inverse operations to isolate the unknown.

Equations with the unknown on both sides

• Move all terms containing the unknown to one side.

• Move constants to the other side.

• Simplify and solve.

Important

• An equation has an equals sign.

• A formula can be rearranged to make a different variable the subject.

• Keep both sides balanced throughout the rearrangement.

• Always check your answer by substituting it back into the original equation.