Use A Sign Chart To Solve The Inequality Calculator
What is an Inequality Calculator?
An inequality calculator is a tool that helps you solve inequalities. Inequalities are mathematical expressions that compare two values, and they use one of the following symbols: >, <, ≤, or ≥. You can use an inequality calculator to find the solutions to an inequality, which are the values that make the inequality true.
What is a Sign Chart?
A sign chart is a way to organize the information you need to solve an inequality. A sign chart is a table that shows the sign of the expression you are working with when you plug in different values. The sign chart helps you determine the solution to an inequality.
How to Use a Sign Chart to Solve an Inequality Calculator?
Here are the steps to use a sign chart to solve an inequality calculator:
- Write the inequality in standard form.
- Find the critical values of the inequality, which are the values that make the expression equal to zero.
- Write the critical values in order from least to greatest on a number line.
- Choose a test value for each interval between the critical values.
- Plug in the test value to the original inequality and determine whether the expression is positive or negative.
- Record the sign of the expression in the corresponding interval on the sign chart.
- Determine the solution to the inequality based on the sign chart.
Example Problem
Let's say you want to solve the inequality: x^2 - 4x > 0.
- Write the inequality in standard form: x^2 - 4x > 0.
- Find the critical values of the inequality: x(x-4) = 0, so the critical values are x = 0 and x = 4.
- Write the critical values in order from least to greatest on a number line:
- Choose a test value for each interval between the critical values:
| Interval | Test Value |
|---|---|
| x < 0 | -1 |
| 0 < x < 4 | 2 |
| x > 4 | 5 |
- Plug in the test value to the original inequality and determine whether the expression is positive or negative:
| Interval | x^2 - 4x > 0 |
|---|---|
| x < 0 | Positive |
| 0 < x < 4 | Negative |
| x > 4 | Positive |
- Record the sign of the expression in the corresponding interval on the sign chart:
- Determine the solution to the inequality based on the sign chart:
The solution to the inequality is: x < 0 or x > 4.
Conclusion
A sign chart is a useful tool to solve an inequality calculator. By following the steps, you can use a sign chart to determine the solution to an inequality. Remember to write the inequality in standard form, find the critical values, write the critical values in order on a number line, choose a test value for each interval, plug in the test value to the original inequality, record the sign of the expression in the corresponding interval on the sign chart, and determine the solution to the inequality based on the sign chart.