Using the Linear Inequality Calculator
Use this to solve threshold or range questions written as ax + b compared with c. Choose the comparison explicitly. The boundary may be included for ≤ and ≥ or excluded for < and >.
Worked example
Use the example inputs below to reproduce this result. These are the form's starting values, not recommended targets. Changing your inputs updates your result above; this worked example stays fixed for comparison. Results are rounded for display.
Example inputs
- a in ax + b
- -2
- b (constant)
- 3
- Comparison
- <
- c (right side)
- 9
Example result
- Solution
- x > -3
- Interval notation
- (-3, ∞)
- Boundary approximation
- -3
- Steps
- Subtract 3 from both sides: -2x < 6. Divide both sides by -2. Reverse the comparison because the divisor is negative. The solution is x > -3.
Method and assumptions
Subtract b and divide by a. Dividing by a negative number reverses the comparison. Zero coefficients produce an always-true or always-false comparison. One real-variable linear inequality; integer inputs only.
Reference: openstax.org — method and further reading
Check the answer in the original problem
After solving, substitute the result into the original equation or relationship where possible. This can catch a sign error or a coefficient entered in the wrong position. Keep the exact inputs available when comparing with another tool, since changing a coefficient or rounding an intermediate value can change the problem being solved.
Common question
Why did the comparison symbol reverse?
Multiplying or dividing both sides by a negative number reverses their order on the number line. For example, −2x < 6 becomes x > −3.