Inequality Calculator

1. Set up the inequality. Enter the coefficient a, constant b, the inequality operator, and the right-hand side c. The calculator solves ax + b [op] c for x. For example: 2x + 3 greater than 7.
2. Apply algebra. Subtract b from both sides: 2x greater than 4. Divide both sides by a: x greater than 2. If a is negative, the inequality sign flips. The calculator handles this automatically and alerts you when a sign flip occurs.
3. Read the solution. The result shows the solution in plain form (x greater than 2), in interval notation ((2, infinity)), and as a number line description. Open circles or parentheses mean the endpoint is excluded; closed circles or brackets mean it is included.
4. Compound inequalities. Switch to the compound tab to solve inequalities of the form lo [op] ax + b [op] hi. This solves both halves simultaneously and returns the intersection as an interval.

Example: 1 less than 3x - 5 less than or equal to 10. Solve: add 5 to all parts: 6 less than 3x less than or equal to 15. Divide by 3: 2 less than x less than or equal to 5. Interval: (2, 5].

Solving ax + b [op] c:
  Step 1: Subtract b from both sides
          ax [op] c - b
  Step 2: Divide both sides by a
          x [op'] (c-b)/a
          IMPORTANT: if a < 0, flip the inequality sign

Example 1: 2x + 3 > 7
  2x > 4      (subtract 3)
  x > 2       (divide by 2, sign stays)
  Solution: x > 2, interval (2, +∞)

Example 2: -3x + 6 ≤ 15
  -3x ≤ 9     (subtract 6)
  x ≥ -3      (divide by -3, FLIP sign)
  Solution: x ≥ -3, interval [-3, +∞)

Example 3: 5x - 2 < 2x + 7
  3x < 9      (subtract 2x, add 2)
  x < 3       (divide by 3)
  Solution: x < 3, interval (-∞, 3)

Compound inequality: 1 < 3x - 5 ≤ 10
  Add 5 to all parts: 6 < 3x ≤ 15
  Divide by 3:        2 < x ≤ 5
  Solution: 2 < x ≤ 5, interval (2, 5]

Interval notation:
  ( ) = open endpoint (number not included)
  [ ] = closed endpoint (number included)
  (-∞, 3) means all x less than 3
  [2, +∞) means all x greater than or equal to 2