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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. (2, 3)
  2. (3, ∞)
  3. (-∞, 2) ∪ (3, ∞)
  4. (2, ∞)

Correct Answer: (-∞, 2) ∪ (3, ∞)

Solution: 

Step 1: Factor: (x - 2)(x - 3) > 0. Step 2: Test intervals: solution is (-∞, 2) ∪ (3, ∞).

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

Practice Questions

Q1
Solve the inequality: x^2 - 5x + 6 > 0.
  1. (2, 3)
  2. (3, ∞)
  3. (-∞, 2) ∪ (3, ∞)
  4. (2, ∞)

Questions & Step-by-Step Solutions

Solve the inequality: x^2 - 5x + 6 > 0.
  • Inequalities – Understanding how to solve quadratic inequalities by factoring and testing intervals.
  • Factoring Quadratics – Recognizing how to factor quadratic expressions to find critical points.
  • Interval Testing – Using test points in intervals to determine where the inequality holds true.
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