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What is the solution of the inequalities \(5x+3 < 8x-9\) and \(2x+20 > 5x + 2\)?

This question was previously asked in
CDS 2 2025 Maths Question Paper (14-Sep-2025)
The correct answer is
\(4 < x < 6\)

To solve the given inequalities, we will address each inequality separately and then find the common solution range for both.

Solve the first inequality: \(5x + 3 < 8x - 9\)

  • Subtract \(5x\) from both sides to get: \(3 < 3x - 9\)
  • Add \(9\) to both sides to simplify: \(12 < 3x\)
  • Divide both sides by \(3\) to isolate \(x\): \(4 < x\)

Solve the second inequality: \(2x + 20 > 5x + 2\)

  • Subtract \(2x\) from both sides to get: \(20 > 3x + 2\)
  • Subtract \(2\) from both sides to simplify: \(18 > 3x\)
  • Divide both sides by \(3\) to isolate \(x\): \(6 > x\) or equivalently \(x < 6\)

Combine the solution of both inequalities:

  • The first inequality gives: \(x > 4\)
  • The second inequality gives: \(x < 6\)
  • Therefore, the common solution is: \(4 < x < 6\)

The correct answer is the range where \(x\) satisfies both inequalities simultaneously, which is:

\(4 < x < 6\)

Conclusion: The correct option

\(4 < x < 6\)

is indeed the valid solution for the given inequalities.

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Important Questions from Mathematical Inequalities

  1. Directions: In the following question assuming the given statements to be true, find which of the conclusion(s) among given conclusions is/are definitely true and then give your answers accordingly.

    Statement:

    Y ≥ C < O ≥ F < R = B

    Conclusions:

    I. B > F

    II. R > C

  2. Directions: In each of the following questions assuming the given statement to be true, find which of the conclusions among given conclusions is / are definitely true and then give your answers accordingly.

    Statement: E < U > L > K ≤ T = H ≤ Q

    Conclusions:

    I. U > H

    II. T ≤ Q

  3. Directions: In the following question assuming the given statements to be True, find which of the conclusion among given conclusions is/are definitely true and then give your answers accordingly.

    Statements: Y > U ≥ Z ≥ K = X ≤ B ≤ A

    Conclusions:

    I. U = X

    II. U > X

  4. Directions: In each of the following questions assuming the given statement to be true, find which of the conclusions among given conclusions is/are definitely true and then give your answers accordingly.

    Statement: S > L < P = T ≥ V > R

    Conclusions:

    I. P > R

    II. S > V

  5. In the question given, relations between different elements are shown in the statements. These statements are followed by two conclusions. Find out which of the given conclusions follow(s) the given statements and select the correct alternative from the given choices.

    Statement:

    L ≥ M = N < O, P < Q ≥ R = S ≥ L

    Conclusion:

    I. Q > M

    II. N = Q

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