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Solve the inequality: x^2 - 5x + 6 ≤ 0.

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Question: Solve the inequality: x^2 - 5x + 6 ≤ 0.

Options:

  1. x ≤ 2 or x ≥ 3
  2. x ≥ 2 and x ≤ 3
  3. x < 2 or x > 3
  4. x > 2 and x < 3

Correct Answer: x ≥ 2 and x ≤ 3

Solution: 

Step 1: Factor the quadratic: (x - 2)(x - 3) ≤ 0. Step 2: The solution is 2 ≤ x ≤ 3.

Solve the inequality: x^2 - 5x + 6 ≤ 0.

Practice Questions

Q1
Solve the inequality: x^2 - 5x + 6 ≤ 0.
  1. x ≤ 2 or x ≥ 3
  2. x ≥ 2 and x ≤ 3
  3. x < 2 or x > 3
  4. x > 2 and x < 3

Questions & Step-by-Step Solutions

Solve the inequality: x^2 - 5x + 6 ≤ 0.
  • Quadratic Inequalities – Understanding how to solve inequalities involving quadratic expressions by factoring and analyzing intervals.
  • Interval Notation – Interpreting and expressing solutions in interval notation, especially for inequalities.
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