PROBLEM SOLVING

Inequalities

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

1 · WHAT YOU NEED TO KNOW

The idea

An inequality describes a range of values rather than one equality.

Picture itFollow what happens to the unknown
2 · THE METHOD

Follow these steps

  1. Solve using inverse operations as for an equation.
  2. Keep the inequality direction when adding or subtracting.
  3. Test boundary values and respect strict or inclusive signs.
3 · WORKED EXAMPLES

See the method in action

Example 1

What is the greatest whole number less than or equal to 10?

  1. “Or equal to” includes 10, so it is the greatest permitted number.
Answer: 10
Example 2

A lift has a weight limit of 38 kg. Each box weighs 6 kg and the trolley weighs 3 kg. What is the least number of boxes that would exceed the limit?

  1. 5 boxes give 33 kg, while 6 give 39 kg; 6 is the first whole number over the limit.
Answer: 6
4 · ELEVENSPRINT TIP

A useful shortcut

Test boundary values and respect strict or inclusive signs.

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.