PROBLEM SOLVING

Two Step Equations

Learn the reliable method for two step equations, then apply it to 11+ exam-style questions.

1 · WHAT YOU NEED TO KNOW

The idea

A two-step equation is solved by undoing operations in reverse order.

Picture itFollow what happens to the unknown
2 · THE METHOD

Follow these steps

  1. Identify the final operation and undo it first.
  2. Undo the remaining operation.
  3. Substitute the value into the original relationship.
3 · WORKED EXAMPLES

See the method in action

Example 1

6 equal bags and 9 loose counters contain 69 counters. How many counters are in each bag?

  1. Remove the 9 loose counters, then divide 60 by 6; each bag contains 10.
Answer: 10
Example 2

A number is reduced by 3; the result is multiplied by 7 to give 14. What was the original number?

  1. Divide by 7 to get x−3=2.
  2. Add 3, so x=5.
Answer: x = 5
4 · ELEVENSPRINT TIP

A useful shortcut

Substitute the value into the original relationship.

5 · COMMON MISTAKES

Watch out for these

6 · TRY IT YOURSELF

Three fresh questions

Ready to check the method? You will get three fresh, validated questions.