AlgebraKS3 / GCSE

Compound inequalities

Solve an inequality with two bounds and represent the interval.

  • Do the same operation to all three parts.
  • If you multiply or divide by a negative number, reverse both inequality signs.
  • Write the final interval with the smallest bound on the left.

Example 1

Write down all of the integer values that satisfy this inequality.

Example 2

Find the solution set and show it on a number line.

Reverse both inequality signs.
Values between -4 and 3. -4 included, 3 excluded.

Your turn

Question 1

Solve.

Check answer
Values between -3 and 4. -3 included, 4 excluded.
Question 2

Solve.

Check answer
Values between 1 and 4. 1 excluded, 4 included.
Question 3

Solve.

Check answer
Reverse both inequality signs.

Reverse both signs when dividing by −2, then write the interval in increasing order.

Values between -3 and 4. -3 excluded, 4 included.
Question 4

Solve.

Check answer
Values between -7 and 11. -7 excluded, 11 included.
Question 5

Solve.

Check answer
Values between 2 and 5. 2 included, 5 included.
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