Solving a Rational Inequality

00:00 3 marks

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  • SL & HL
  • Tier 3
  • Sign analysis
  • Critical point analysis
  • Solving rational inequalities

Solve the inequality \(\frac{2x-3}{x+4} > 0\) and express your answer in interval notation.

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Hint

Identify the critical values where the numerator or denominator equals zero. These values divide the number line into intervals. Test a point within each interval to determine the sign of the expression.

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Complete Answer

\( x \in (-\infty, -4) \cup \left(\frac{3}{2}, \infty \right) \)

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