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Algebra · Inequalities

Solve 2x - 5 < 3

2 x - 5 < 3

Step by step

  1. 2 x - 5 < 3

    Start from the inequality.

  2. 2 x - 8 < 0

    Move everything to the left so we compare against 0.

  3. x = 4

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

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

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

  5. \left(-\infty, 4\right)

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

  6. -\infty < x \wedge x < 4

    The same answer written as inequalities.

Reveal the answer
-\infty < x \wedge x < 4