Solving Linear Inequalities

This inequality calculator solves ax + b ◯ c by isolating x: subtract b from both sides, then divide by a. The single rule that differs from equation solving — flip the sign when a is negative — is applied and reported automatically.

The Flip Rule

Inequalities reverse when both sides are multiplied or divided by a negative number. For 2x + 3 < 11, dividing by positive 2 keeps the direction and yields x < 4. Had the coefficient been −2, the solution would flip to x > −4.

Testing the Solution

Verify by plugging in a point: x = 3 gives 9 < 11 ✓, while x = 5 gives 13 < 11 ✗. Any value on the correct side of the boundary satisfies the inequality — that is the whole solution set.