Linear Inequality Calculator: Solve ax + b < c with Steps and Number Line
Enter a, b, c and pick <, ≤, > or ≥. You get the solution, the interval and a number line, with a clear note when the sign flips.
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Solution
x > −3
Sign flipped- Interval notation
- (−3, ∞)
- Boundary value
- −3
We divided by a negative number (−2), so the inequality sign was reversed.
Show working
- −2x + 5 < 11
- −2x < 11 − 5 = 6
- ÷ (−2) → < ⇒ >
- x > −3
How to use
- Write your inequality as ax + b (sign) c.
- Enter a, b and c and choose the sign.
- Read x and the interval; check the number line.
Good to know
Solve it like an equation: subtract b from both sides, then divide by a. The one extra rule: dividing or multiplying both sides by a negative number reverses the inequality sign (< becomes >, ≤ becomes ≥).
Why the flip? Multiplying by −1 mirrors the number line: 2 < 3 but −2 > −3. So −2x < 6 means x > −3, not x < −3.
Interval notation: x > −3 is (−3, ∞); x ≥ 1/3 is [1/3, ∞). A round bracket (open dot) means the end value is not included; a square bracket (filled dot) means it is.
Questions
When do I flip the inequality sign?
Only when you multiply or divide both sides by a negative number.
How do I solve −2x + 5 < 11?
−2x < 6, then divide by −2 and flip the sign: x > −3.
What is the difference between < and ≤ on the number line?
< uses an open (hollow) dot because the end value is excluded; ≤ uses a filled dot because it is included.
What if a = 0?
Then x disappears. The statement is either always true (every x works) or never true (no solution).
Is my data stored or sent anywhere?
No. The calculation runs entirely in your browser; nothing you type leaves your device.