Modulus (Leaving Cert Mathematics): Flashcards

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Absolute (Modulus) Equations
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What does absolute value represent?

Magnitude of a number; distance from origin

Key property of modulus output

Always positive

∣x∣|x| when x≥0x \ge 0

xx

∣x∣|x| when x<0x < 0

−x-x

Value of ∣−3∣|-3|

33

Value of ∣3∣|3|

33

Solutions to ∣d∣=5|d| = 5

d=±5d = \pm 5

Method 1: Solving ∣d∣=5|d| = 5 intuitively

Set d=±5d = \pm 5 (both positive and negative)

Method 2: Solving modulus equations

Square both sides

Why squaring eliminates modulus

Squaring always gives positive value

Solutions to ∣2x−1∣=x|2x-1| = x

x=1x = 1 and x=13x = \frac{1}{3}

Alternative method for ∣2x−1∣=x|2x-1| = x

Set 2x−1=±x2x-1 = \pm x and solve both cases

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