Inequalities involving absolute value and square roots (HSC SSCE Mathematics Extension 1): Flashcards
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What does absolute value measure on the number line?
What does absolute value measure on the number line?
It measures the distance from zero, always non-negative.
What is a square root?
What is a square root?
A number that, when squared, gives the original number.
What happens when you multiply an inequality by a negative?
What happens when you multiply an inequality by a negative?
The inequality sign reverses direction.
What is the domain for square roots?
What is the domain for square roots?
Only non-negative numbers to avoid undefined results.
How do you solve |x| < 4?
How do you solve |x| < 4?
Form two inequalities: x < 4 and x > -4.
What is the result of squaring both sides of an inequality?
What is the result of squaring both sides of an inequality?
It must be done carefully to avoid mistakes.
What is a common mistake in solving inequalities?
What is a common mistake in solving inequalities?
Omitting domain checks can lead to errors.
How do you find solutions graphically?
How do you find solutions graphically?
Sketch graphs and find intersection points.
What is case-by-case analysis in absolute values?
What is case-by-case analysis in absolute values?
Analyzing different cases for |x| < b.
What should you check when squaring both sides?
What should you check when squaring both sides?
Always check the domain to avoid invalid solutions.