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Inequalities - Beginner-Intermediate Level: direct inequalities BEGINNER-INTERMEDIATE

This deep dive ★ worksheet contains 20 beginner-intermediate-level inequalities problems. Worksheet 11 of 30 focuses on direct inequalities. Practice symbolic inequalities, chain inequalities, inequality solving with our step-by-step solutions. Difficulty: building on fundamentals with moderate challenges. Recommended for developing learners.

📝 Worksheet 11 of 30 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Beginner-intermediate level

What you'll learn in this worksheet:
Your progress through Inequalities
Worksheet 11 of 30 (36% complete)

Question 1

Statements: I. F ≥ B > C II. C < A ≤ D Which conclusion is definitely false?
From the statements, F < D contradicts the established relationships and is definitely false.
reverse, mixed, direction

Question 2

Directions: % means ≤, @ means >, & means =, $ means ≥, # means < Statement: R # U & S $ P Which conclusion follows?
Decoding: R < U → < U = S → = S ≥ P. Therefore, No definite conclusion.
coded, symbols, decoding

Question 3

Statements: B > G = A ≥ D Conclusion: B > D Is the conclusion true?
From B > G = A ≥ D, using transitivity, B > D is definitely true.
basic, comparison, transitive

Question 4

Statement: Z ≤ X ≤ V Conclusions: I. Z < V II. Z = V Which follows?
From Z ≤ X ≤ V, either Z < V or Z = V. Hence either I or II follows.
either-or, logical, possibility

Question 5

Statements: U > Q; Q > W; Q > V; W = P; V ≥ R Which of the following is definitely true?
Analyzing the chain: U > Q; Q > W; Q > V; W = P; V ≥ R. Therefore, U > P is definitely true.
complex, chain, multi-step

Question 6

Statements: A ≥ E > H ≥ G Conclusion: E = G Is the conclusion true?
From A ≥ E > H ≥ G, we cannot determine the exact relationship between E and G.
basic, comparison, transitive

Question 7

Statements: I. A ≥ F > E II. E ≥ G > D Which conclusions definitely follow?
Combining statements: A ≥ F > E ≥ G > D. Therefore, I, II, and III definitely follow(s).
compound, multiple, chain

Question 8

Statements: A ≥ G > D ≥ C Conclusion: C > A Is the conclusion true?
From A ≥ G > D ≥ C, C > A contradicts the given inequalities, so it's false.
basic, comparison, transitive

Question 9

Statements: F ≥ B ≥ G ≥ C Conclusion: B = C Is the conclusion true?
From F ≥ B ≥ G ≥ C, we cannot determine the exact relationship between B and C.
basic, comparison, transitive

Question 10

Statement: Z ≤ W ≤ Y Conclusions: I. Z < Y II. Z = Y Which follows?
From Z ≤ W ≤ Y, either Z < Y or Z = Y. Hence either I or II follows.
either-or, logical, possibility

Question 11

Statements: Q > U ≥ S; P ≤ S < T; T = W; W ≥ V Which of the following is definitely true?
Analyzing the chain: Q > U ≥ S; P ≤ S < T; T = W; W ≥ V. Therefore, S < W is definitely true.
complex, chain, multi-step

Question 12

Statement: Q ≥ S > M = O ≥ P Which conclusions are definitely true?
From Q ≥ S > M = O ≥ P, we can derive: Q > M. These conclusions definitely follow.
multiple, evaluation, analysis

Question 13

Statements: I. F ≥ A > B II. B ≥ E > D Which conclusions definitely follow?
Combining statements: F ≥ A > B ≥ E > D. Therefore, I, II, and III definitely follow(s).
compound, multiple, chain

Question 14

Arrange the elements D, B, E, A, C based on these clues: - D > B - A > C - E < B - E > A Which element is the largest?
From the clues: D > B > E > A > C. Therefore, D is the largest.
puzzle, arrangement, ordering

Question 15

Directions: # means <, $ means ≥, % means ≤, & means =, @ means > Statement: U # R $ P % S Which conclusion follows?
Decoding: U < R → < R ≥ P → ≥ P ≤ S. Therefore, No definite conclusion.
coded, symbols, decoding

Question 16

Statements: D > A = E ≥ G Conclusion: G > D Is the conclusion true?
From D > A = E ≥ G, G > D contradicts the given inequalities, so it's false.
basic, comparison, transitive

Question 17

Statements: C ≥ H ≥ G ≥ B Conclusion: C ≥ B Is the conclusion true?
From C ≥ H ≥ G ≥ B, using transitivity, C ≥ B is definitely true.
basic, comparison, transitive

Question 18

Statements: I. B = C < D II. D ≤ A = G Which conclusions definitely follow?
Combining statements: B = C < D ≤ A = G. Therefore, Only I definitely follow(s).
compound, multiple, chain

Question 19

Arrange the elements D, A, B, C, E based on these clues: - B < A - B > C - D > A - C > E Which element is the largest?
From the clues: D > A > B > C > E. Therefore, D is the largest.
puzzle, arrangement, ordering

Question 20

Statement: X ≥ Z ≥ Y Conclusions: I. X > Y II. X = Y Which follows?
From X ≥ Z ≥ Y, either X > Y or X = Y. Hence either I or II follows.
either-or, logical, possibility
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