Inequality Solver

An inequality compares two expressions using <, ≤, > or ≥, and its solution is usually a range of values. This inequality solver collects the x terms, divides by the coefficient, flips the sign when dividing by a negative number, and shows the answer in interval notation and on a number line.

Try:

How to use the inequality solver

  1. Write your inequality as ax + b ? cx + d.
  2. Enter a, b, c, d and choose the sign.
  3. Press Calculate to see the solution, the interval and the number line.

Formula

kx<m,  k<0⇒x>mkkx < m,\; k < 0 \Rightarrow x > \frac{m}{k}

Worked example: 3x − 4 < x + 6

  • a (x on the left): 3
  • b (number on the left): -4
  • Sign: <
  • c (x on the right): 1
  • d (number on the right): 6

✓ Answer checked

x<5x < 5
Interval notation
(−∞,  5)(-\infty,\; 5)
−20246810125
An open circle means the boundary is not included; the shaded ray shows every solution.
Step-by-step working (3 steps)

  1. Write the inequality

    Collect everything in the form ax + b ? cx + d.

    3x−4<x+63x - 4 < x + 6

  2. Collect x terms on the left and numbers on the right

    Adding or subtracting the same amount on both sides keeps the sign.

    2x<102x < 10

  3. Divide

    Divide both sides by 2.

    x<5x < 5
Formulas used
If k<0:  kx<m  ⟺  x>mk\text{If } k < 0: \; kx < m \iff x > \frac{m}{k}
How this was checked
  • ✓ x = 4 satisfies the original inequality, x = 6 does not, and the boundary 5 is excluded.

Frequently asked questions

When do I flip the inequality sign?

When you multiply or divide both sides by a negative number. For example, −2x ≥ 6 becomes x ≤ −3.

What does an open circle mean on a number line?

The boundary value is not included (< or >). A filled dot means it is included (≤ or ≥).

How do I write the answer in interval notation?

x < 5 is (−∞, 5); x ≥ 2 is [2, ∞). Square brackets include the end, round brackets exclude it.

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