Solving Inequalities (HSC SSCE Mathematics Advanced): Quizzes

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Solving Inequalities
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What is created when the equals sign in an equation is replaced by <<, >>, ≤\leq, or ≥\geq?

An inequation

Which statement is true for all values of xx?

x2≥0x^2 \geq 0

Using the geometric interpretation, a<ba < b means aa is where relative to bb on the number line?

To the left of bb

What happens to the inequality symbol when dividing −2x<6-2x < 6 by −2-2?

It reverses to give x>−3x > -3

What is the solution to 20>2−3x≥820 > 2 - 3x \geq 8?

−6<x≤−2-6 < x \leq -2

What is the solution to x2>9x^2 > 9?

x>3x > 3 or x<−3x < -3

What does ∣x−a∣|x - a| represent on the number line?

The distance from xx to aa

How is ∣f(x)∣<a|f(x)| < a rewritten algebraically?

−a<f(x)<a-a < f(x) < a

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

x=−3x = -3 or x=7x = 7

If aa is negative, what solutions does ∣f(x)∣=a|f(x)| = a have?

No solutions

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