Modulus Inequalities (Leaving Cert Mathematics): Flashcards

📚Flashcards
Revision NotesModel AnswersQuizzesFlashcardsExam Questions
Modulus Inequalities
Sign up to keep revising.Create a free account to study more flashcards and track your progress.

Practise the cards

10 cards from this deck

Show

General form of a modulus inequality

∣ax+b∣|ax+b| where aa, bb are constants

First step to solve ∣2x−3∣<5|2x-3|<5

Square both sides

(2x−3)2<25(2x-3)^2<25 simplifies to

4x2−12x−16<04x^2-12x-16<0

Factored form of 4x2−12x−16<04x^2-12x-16<0

(x−4)(x+1)<0(x-4)(x+1)<0

What is the region test method?

Pick values outside and between critical points to test inequality

Critical points in (x−4)(x+1)<0(x-4)(x+1)<0

−1-1 and 44

Does x=0x=0 satisfy ∣2x−3∣<5|2x-3|<5?

Yes, 3<53<5

Does x=5x=5 satisfy ∣2x−3∣<5|2x-3|<5?

No, 7≮57 \not< 5

Does x=−2x=-2 satisfy ∣2x−3∣<5|2x-3|<5?

No, 7≮57 \not< 5

Solution to ∣2x−3∣<5|2x-3|<5

−1<x<4-1<x<4

Explore Leaving Cert Mathematics Revision Notes by Topics

Inequalities

Modulus

Inequality Proofs & Discriminants

Explore Leaving Cert Mathematics Model Answers by Topics

Inequalities

Modulus

Inequality Proofs & Discriminants

Explore Leaving Cert Mathematics Quizzes by Topics

Inequalities

Modulus

Inequality Proofs & Discriminants

Explore Leaving Cert Mathematics Exam Questions by Topics

Inequalities

Modulus

Inequality Proofs & Discriminants

Join 100,000+ Leaving Cert students studying Flashcards with us.

Select your subjects, and get access to A+ resources today.