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Algebra · Inequalities

Solve x^2 + x - 6 < 0

x^{2} + x - 6 < 0

Step by step

  1. x^{2} + x - 6 < 0

    Start from the inequality.

  2. x^{2} + x - 6 < 0

    Move everything to the left so we compare against 0.

  3. x = -3, x = 2

    Find the critical points: where the expression equals 0 (or is undefined). They split the number line into test intervals.

  4. (-\infty,\, -3): +\;\;(-3,\, 2): -\;\;(2,\, \infty): +

    Test a point inside each interval to find the sign of the expression there.

  5. \left(-3, 2\right)

    Keep the intervals whose sign satisfies the inequality (closed endpoints for ≤ / ≥, open for < / >).

  6. -3 < x \wedge x < 2

    The same answer written as inequalities.

Reveal the answer
-3 < x \wedge x < 2