Modulus Functions - Solving Equations (AQA A-Level Mathematics): Flashcards

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Modulus Functions - Solving Equations
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Output of modulus function

Non-negative value of any real number

Notation for modulus of xx

x|x|

Definition of x|x|

xx if x0x \geq 0; x-x if x<0x < 0

Approach to solve modulus equations

Consider different cases based on definition

Solutions to x=4|x| = 4

x=4x = 4 or x=4x = -4

Why x=4|x| = 4 has two solutions

Modulus removes any negative sign

Solve 2x3=5|2x - 3| = 5 when 2x302x - 3 \geq 0

x=4x = 4

Solve 2x3=5|2x - 3| = 5 when 2x3<02x - 3 < 0

x=1x = -1

Solution to x1=2x+3|x - 1| = |2x + 3|

x=4x = -4

After solving modulus cases, what must you check?

Validity of solutions in original equation and case conditions

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