Algebra and proofAdditional / Further Maths

Solving linear inequalities

Solve an inequality and reverse its sign when multiplying or dividing by a negative.

  • Solve inequalities using the same balanced steps as equations.
  • Reverse the inequality sign if you multiply or divide both sides by a negative number.

Example 1

Solve the inequality.

Divide both sides by . Reverse the inequality sign because this number is negative.
Values above -5. -5 included.

Example 2

Solve the inequality.

Multiply both sides by . Reverse the inequality sign because this number is negative.
Values below -4. -4 included.

Your turn

Question 1

Solve and represent the solution on a number line.

Check answer
Values below 4. 4 excluded.
Question 2

Solve and represent the solution on a number line.

Check answer
Values above 3. 3 included.
Question 3

Solve and represent the solution on a number line.

Check answer
Reverse the inequality sign.

Divide by −3 and reverse the inequality sign.

Values above -4. -4 included.
Question 4

Solve and represent the solution on a number line.

Check answer
Reverse the inequality sign.

Divide by −2 and reverse the inequality sign.

Values below 3. 3 excluded.
Question 5

Solve the inequality.

Check answer
Values below 4. 4 included.
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