Compound Inequality Calculator

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 Compound Inequality

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A compound inequality is an inequality that combines two or more inequalities connected by the words "and" or "or". Solving compound inequalities involves finding the values of the variable that satisfy all of the inequalities in the compound inequality.

Use this calculator to solve compound inequalities.

What is a Compound Inequality?

A compound inequality is an inequality containing two or more inequalities joined with the words "and" or "or". There are three types of compound inequalities:

• Conjunctions: Compound inequalities connected by "and".
• Disjunctions: Compound inequalities connected by "or".
• Absolute Value: An inequality containing an absolute value.

How to Use the Calculator

1. Enter the first inequality in the first input field, using the variable x.
2. Select whether the compound inequality is a conjunction or a disjunction using the dropdown menu.
3. Enter the second inequality in the third input field, using the variable x.
4. Click the "Calculate" button to see the solution.

Formula

A conjunction can be written in the form:

a < x < b and c < x < d

A disjunction can be written in the form:

a < x < b or c < x < d

An absolute value inequality can be written in the form:

|ax + b| < c

Example

Solve the following compound inequality: 2x + 3 < 5 and 4x - 1 > 11.

1. Enter "2x + 3 < 5" in the first input field.
2. Select "and" from the dropdown menu.
3. Enter "4x - 1 > 11" in the third input field.
4. Click the "Calculate" button.

The solution is:

2 < x < 3

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