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

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Modulus Functions - Solving Equations
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What does the modulus function give for any real number?

The non-negative value

How is the modulus of xx denoted?

∣x∣|x|

For x<0x < 0, what is ∣x∣|x| equal to?

−x-x

What are the solutions to ∣x∣=4|x| = 4?

x=4x = 4 or x=−4x = -4

How many cases must be considered when solving ∣2x−3∣=5|2x - 3| = 5?

Two cases

For ∣2x−3∣=5|2x - 3| = 5 when 2x−3≥02x - 3 \geq 0, what is the solution?

x=4x = 4

What are the solutions to ∣2x−3∣=5|2x - 3| = 5?

x=4x = 4 and x=−1x = -1

What is the solution to ∣x−1∣=∣2x+3∣|x - 1| = |2x + 3|?

x=−4x = -4

In Example 3, why is x=−4x = -4 invalid in Case 1?

It contradicts x≥1x \geq 1

What is the first step when solving modulus equations?

Split into cases based on sign changes

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