Modulus Inequalities (Leaving Cert Mathematics): Quizzes

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Modulus Inequalities
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What form do modulus inequalities involve?

∣ax+b∣|ax+b|

What is the first step to solve ∣2x−3∣<5|2x-3|<5?

Square both sides

What is (2x−3)2(2x-3)^2 expanded?

4x2−12x+94x^2-12x+9

What is the factorised form of 4x2−12x−16<04x^2-12x-16<0?

(x−4)(x+1)<0(x-4)(x+1)<0

What are the critical values from (x−4)(x+1)<0(x-4)(x+1)<0?

−1-1 and 44

What is the purpose of the region test?

Pick values to check which regions work

When testing x=0x=0 in ∣2x−3∣<5|2x-3|<5, what value is compared to 55?

33

Does x=5x=5 satisfy ∣2x−3∣<5|2x-3|<5?

No, because 7≮57\not<5

What is the solution to ∣2x−3∣<5|2x-3|<5?

−1<x<4-1<x<4

Which region satisfies the inequality (x−4)(x+1)<0(x-4)(x+1)<0?

Between −1-1 and 44

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