Exam Questions - Modulus inequalities

Exam Questions - Modulus inequalities

Common Question Formats

• Solving inequalities involving modulus of linear expressions.
• Identifying the solution set to a given modulus inequality.
• Sketching the graph of a modulus function to illustrate inequalities.
• Applying the knowledge of complementary intervals for modulus inequalities.

Strategies for Addressing Questions

• For inequalities in the form of

  ax + b

  < c, be clear that the solution lies within c units of -b/a on the number line.

• When inequalities are presented in a format of

  ax + b

  > c, know that solutions lie outside c units of -b/a.

• To illustrate modulus inequalities, plot the function y =

  ax + b

  and work out the x-values where the function meets the y-value c.

• As a rule, the complementary intervals correspond to flipping the inequality symbol. If x < a or x > b corresponds to the original solution, x ≥ a and x ≤ b would be the complementary interval.

Potential Pitfalls

• The common mistake is to treat the modulus inequality as a regular inequality. Keep in mind that the modulus of a number is always positive, and this is what functionally distinguishes a modulus inequality from any other inequality.
• Modulus inequalities also have two solutions, one for x < 0 and one for x > 0, which should both be noted.

• Avoid mistaking the required solution set. For

  ax + b

  < c, the solution is a finite interval on the number line, whereas for

  ax + b

  > c, solutions are two infinite intervals.

• Plotting modulus functions incorrectly can be misleading, ensure that for

  x

  , the graph should always be above the x-axis.

• Understanding the concept of complementary intervals and using it properly is key. Not interpreting these intervals correctly might lead to incorrect solution sets.

Remember, the more you interact with modulus inequalities, the better you get. Practice and understanding are key. Good luck with your revision!