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Solve the inequality: x^2 + 2x - 8 < 0.

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Question: Solve the inequality: x^2 + 2x - 8 < 0.

Options:

  1. -4 < x < 2
  2. x < -4 or x > 2
  3. x > -4 and x < 2
  4. x < 2

Correct Answer: -4 < x < 2

Solution: 

Step 1: Factor: (x + 4)(x - 2) < 0. Step 2: Critical points are x = -4 and x = 2. Step 3: Test intervals: -4 < x < 2.

Solve the inequality: x^2 + 2x - 8 < 0.

Practice Questions

Q1
Solve the inequality: x^2 + 2x - 8 < 0.
  1. -4 < x < 2
  2. x < -4 or x > 2
  3. x > -4 and x < 2
  4. x < 2

Questions & Step-by-Step Solutions

Solve the inequality: x^2 + 2x - 8 < 0.
  • Inequalities – Understanding how to solve quadratic inequalities by factoring and testing intervals.
  • Critical Points – Identifying points where the expression equals zero to determine intervals for testing.
  • Interval Testing – Using test points in the intervals created by critical points to determine where the inequality holds.
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