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Definition

The greater than symbol (>) is a mathematical operator used to compare two values and indicate that one value is larger than the other. It is a fundamental concept in algebra that is applied in various contexts, including solving linear inequalities, compound inequalities, absolute value inequalities, graphing linear inequalities in two variables, graphing systems of linear inequalities, solving rational inequalities, and solving quadratic inequalities.

5 Must Know Facts For Your Next Test

1. The greater than symbol (>) is used to indicate that one value is larger than another value.
2. When solving linear inequalities, the greater than symbol is used to represent the solutions where the variable is greater than a specific value.
3. In the context of compound inequalities, the greater than symbol is used to connect two or more inequalities, creating a range of acceptable values.
4. Graphing linear inequalities in two variables involves using the greater than symbol to represent the region of the coordinate plane where the inequality is true.
5. When solving rational inequalities, the greater than symbol is used to compare the numerator and denominator expressions.

Review Questions

• Explain how the greater than symbol (>) is used in the context of solving linear inequalities.
  • When solving linear inequalities, the greater than symbol (>) is used to represent the solutions where the variable is greater than a specific value. For example, in the inequality $x > 5$, the solutions are all the values of $x$ that are larger than 5. The greater than symbol indicates that the variable must be strictly greater than the given value to satisfy the inequality.
• Describe the role of the greater than symbol (>) in graphing linear inequalities in two variables.
  • When graphing linear inequalities in two variables, the greater than symbol (>) is used to represent the region of the coordinate plane where the inequality is true. For instance, the inequality $2x + y > 4$ would be graphed by shading the half-plane above the line $2x + y = 4$, as the points in this region satisfy the inequality.
• Analyze how the greater than symbol (>) is used in the context of solving rational inequalities.
  • In the process of solving rational inequalities, the greater than symbol (>) is used to compare the numerator and denominator expressions. The goal is to find the values of the variable that make the inequality true. For example, in the inequality $\frac{x-2}{x+3} > 0$, the greater than symbol is used to determine the values of $x$ that make the numerator and denominator have the same sign, resulting in a positive rational expression.

Related terms

Inequality:

A mathematical statement that compares two expressions and indicates that one is greater than, less than, or not equal to the other.

Linear Inequality:

An inequality that involves a linear expression, such as $ax + b > c$, where $a$, $b$, and $c$ are constants.

Compound Inequality:

An inequality that combines two or more inequalities using the logical connectives 'and' or 'or'.