Calculator Form
Example Data Table
| a | b | Sign | c | Range | Expected interval |
|---|---|---|---|---|---|
| 2 | 3 | <= | 11 | -5 to 8 | (-∞, 4] |
| -4 | 8 | > | 0 | -3 to 5 | (-∞, 2) |
| 5 | -10 | >= | 15 | 0 to 8 | [5, ∞) |
Formula Used
The calculator uses the standard linear inequality form:
ax + b sign c
First subtract b from both sides:
ax sign c - b
Then divide by a:
x sign (c - b) / a
If a is negative, the inequality sign reverses. For example, less than becomes greater than. If a equals zero, the variable term disappears. Then the calculator compares b with c and decides whether every real value works or no value works.
How to Use This Calculator
- Enter coefficient a for the variable term.
- Enter constant b for the left side expression.
- Select the inequality sign.
- Enter c for the right side value.
- Set the x range and table step.
- Choose whether to show all rows, true rows, or false rows.
- Press calculate to view the answer above the form.
- Use CSV or PDF export for records, worksheets, or reports.
About Linear Inequality Tables
Clear Testing of x Values
A linear inequality table helps you test many values of x against one rule. The rule usually has the form ax + b compared with c. Each table row substitutes one x value. Then it calculates the left side, compares it with the right side, and marks the statement as true or false.
Why the Boundary Matters
The boundary is the point where the related equation becomes equal. It is found by solving ax + b = c. This point splits the number line. Values on one side usually satisfy the inequality. Values on the other side usually fail it. Closed signs include the boundary. Open signs exclude it.
Advanced Table Control
This calculator gives more control than a simple solver. You can change the variable letter, decimal precision, x range, and step size. You can also filter the table. This is useful when a teacher wants only solution values, or when a student wants to inspect false cases.
Sign Reversal Rule
The most common mistake happens when dividing by a negative number. In that case, the inequality sign must reverse. The calculator shows this step in the working notes. This makes the result easier to audit and explain.
Practical Learning Uses
Tables are helpful for graphing, homework checking, classroom demonstrations, and worksheet creation. They connect algebra with number line thinking. They also show that an inequality is not only one answer. It is often a whole set of values.
Export Benefits
The CSV option is useful for spreadsheets. The PDF option is useful for printable records. Both exports help students and tutors save the calculated table without copying rows by hand.
FAQs
1. What is a linear inequality?
A linear inequality compares a first degree expression with another value. It uses signs like less than, greater than, less than or equal, and greater than or equal.
2. What does the table show?
The table shows tested x values, the calculated left side, the right side, the difference, and whether each statement is true or false.
3. Why does the sign flip?
The sign flips when both sides are divided by a negative number. This keeps the inequality statement logically correct.
4. What is the boundary value?
The boundary value is where the related equation becomes equal. It separates likely true and false regions on the number line.
5. Can this handle equalities?
Yes. Select the equality sign to test where the linear expression equals the right side value.
6. What happens when a is zero?
The variable disappears. The calculator compares the remaining constants and decides whether all real values work or no values work.
7. Why use a step value?
The step controls spacing between tested x values. Smaller steps create a more detailed table, while larger steps keep the table shorter.
8. What are CSV and PDF exports for?
CSV export helps with spreadsheets. PDF export helps with printing, sharing, and saving worked inequality tables.