Solving Equations with Modulus Functions (Cambridge International AS Mathematics)

Modulus Functions - Solving Equations

Solving equations with modulus functions

How do I sketch modulus equations?

• Two non-parallel straight-line graphs would intersect once
• If a modulus is involved there could be more than one intersection
• Deducing where these intersections are is crucial to solving equations

How do I solve modulus equations?

• STEP 1 Sketch the graphs including any modulus (reflected) parts

  • (see Modulus Functions – Sketching Graphs)

• STEP 2 Locate the graph intersections

• STEP 3 Solve the appropriate equation(s) or inequality

  • For $\vert \mathrm{f} ( x ) \vert = \vert \mathrm{g} ( x ) \vert$ the two possible equations are $f(x)=g(x)$ and $f(x)=-g(x)$

Exam Hint

• Sketching the graphs is important as solving algebraically can lead to invalid solutions.
• For example, x = 1 is a solution to $x-4=2x-5$ but it is not a solution to $\vert x - 4 \vert = 2 x - 5$ (substitute x = 1 into both sides and see why it does not work).

Worked Example