Solving Equations with Inverse Operations

Solving Equations with Inverse Operations

A flow diagram can be run forwards to make an output and backwards to find an input. To solve an equation, undo operations in reverse order. Addition is undone by subtraction, multiplication by division, and vice versa. Keep the equality balanced and check your result in the original rule.

Worked example

A machine multiplies by 3 then adds 4 to make 19. Work backwards: $19-4=15$, then $15\div3=5$. The input was 5.

Exam method

1. Identify the last forward operation. 2. Apply its inverse. 3. Continue backward until the input is alone; substitute to check.