Analyze valid intervals for inequality expressions with structured inputs. Combine denominator, root, and log rules. Build clean domain results with confidence and clarity.
| Case | Denominator | Even Root | Log Argument | Computed Domain |
|---|---|---|---|---|
| Example 1 | x - 4 ≠ 0 | x² - 5x + 6 ≥ 0 | 2x - 3 > 0 | (3, 4) ∪ (4, ∞) |
| Example 2 | x + 1 ≠ 0 | x² - 1 ≥ 0 | x - 2 > 0 | (2, ∞) |
| Example 3 | 2x - 8 ≠ 0 | x² - 9 ≥ 0 | x + 5 > 0 | [3, 4) ∪ (4, ∞) |
The calculator finds where every expression part is valid.
In symbols:
Domain = (denominator valid set) ∩ (root valid set) ∩ (log valid set)
A domain of inequalities calculator helps you find where an inequality is valid before solving it. This step prevents undefined values. It also keeps the algebra accurate. Many students lose marks by ignoring domain limits too early.
Inequality expressions often contain fractions, roots, and logarithms. Each part adds a rule. A denominator can never be zero. An even root needs a radicand that is zero or positive. A logarithm needs an argument greater than zero.
This calculator combines those rules into one final set. It checks denominator restrictions first. Then it tests the even root condition. After that, it applies the logarithm condition. The final answer is the overlap of all valid intervals.
Interval notation is useful because it summarizes many values in a compact form. Open brackets show excluded endpoints. Closed brackets show included endpoints. Union symbols connect separate valid regions. This is very helpful in algebra, precalculus, and higher mathematics.
You can use this tool for classroom practice, homework checks, and exam revision. It is useful when working with rational inequalities, radical inequalities, and logarithmic inequalities. It also helps when building graph-ready domain sets for further analysis.
Always check the domain before moving signs, squaring both sides, or multiplying by unknown expressions. Those steps can create errors if restrictions are ignored. When the domain is clear, the solving path becomes safer, faster, and easier to explain.
A clear domain gives meaning to every later step in an inequality problem. Use the calculator to identify valid values, review restrictions, and export a quick summary for reference. It supports cleaner reasoning and more reliable mathematical results.
It finds the values of the variable for which the inequality expression is defined. It does not only solve the inequality. It first checks whether fractions, roots, and logarithms are mathematically valid.
Division by zero is undefined in real numbers. If any denominator becomes zero, that value must be removed from the domain, even if later algebra appears to allow it.
For real-number work, square roots and other even roots need inputs that are zero or positive. Negative radicands would produce non-real values, so they are excluded from the domain.
Real logarithms are defined only for positive arguments. Zero and negative inputs are not allowed. That is why the calculator uses a strict greater-than condition for logarithmic parts.
Yes. You can keep only the denominator, root, or log option active. The calculator will then build the domain from that selected condition alone.
The full domain shows every valid real interval. The visible domain limits that answer to the range you selected, which helps when checking examples or preparing graphs.
It focuses on domain analysis. That is the valid input set for the expression. You can use the result before applying sign charts, interval tests, or further solving steps.
Check it at the beginning. Early domain work prevents invalid steps, removes impossible values, and makes the final inequality solution cleaner and more trustworthy.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.