Calculated result
Answer
Steps
Graph
Solid boundaries include equality. Dashed boundaries exclude equality.
Calculation history
Formula used
Linear boundary: ax + by = c
Intersection: solve both boundary equations together.
Objective: Z = px + qy
Each inequality becomes a boundary and a valid side. The calculator intersects every valid region for AND logic. OR logic combines every accepted region instead.
Dividing by a negative reverses the inequality direction. Strict signs create open boundaries in one dimension. They create dashed boundaries on two-dimensional graphs.
How to use this calculator
- Choose automatic or manual variable mode.
- Enter one inequality in each row.
- Select AND or OR combination logic.
- Set the numeric search range and precision.
- Optionally enter a point or objective function.
- Press Calculate system to view results.
- Review steps, graph, vertices, and warnings.
- Copy, print, or export the calculation.
Example data
| Example | System | Expected result type |
|---|---|---|
| Compound interval | 2x - 3 > 1; x + 4 <= 10 | Intersection interval |
| Linear feasible region | 2x + y <= 8; x - y > 1; x >= 0; y >= 0 | Shaded polygon |
| Quadratic system | x^2 - 9 <= 0; x > 1 | Bounded interval |
| Absolute value | abs(x - 2) < 5; x >= 0 | Open and closed endpoints |
| Rational restriction | 1/(x - 2) > 0; x < 8 | Split intervals |
| Optimization | x + y <= 6; x >= 0; y >= 0 | Best feasible vertex |
Frequently asked questions
What are simultaneous inequalities?
They are inequalities considered as one connected system. A solution must follow the selected logical rule. AND requires every condition to hold.
Does the calculator support strict inequalities?
Yes, it supports less-than and greater-than signs. Strict endpoints appear open in interval results. Their graph boundaries use dashed lines.
Can it solve nonlinear inequalities?
Yes, one-variable nonlinear systems use numeric root isolation. Two-variable nonlinear systems use sampled region shading. Results may be approximate near difficult boundaries.
How are rational restrictions handled?
Undefined points are excluded from accepted intervals. The solver checks discontinuities during numeric scanning. Warnings identify approximate domain restrictions.
What does an empty feasible region mean?
No point satisfies the complete AND system. Conflicting conditions often cause this outcome. Review each boundary and logical selection carefully.
Can I maximize or minimize an objective?
Yes, linear two-variable systems support vertex optimization. Enter an objective like 3x plus 5y. Choose maximize or minimize before calculating.
Why can a region be unbounded?
An unbounded region extends beyond the selected graph range. The calculator marks likely unbounded solutions. Increase the graph range for confirmation.
Can I test a specific point?
Yes, enter x, y, and optional z coordinates. The result shows every substituted expression value. It also identifies failed inequalities.
Are exported values exact?
Linear coefficients are evaluated with floating-point arithmetic. Nonlinear roots are numeric approximations. Increase precision when more displayed digits are required.