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Definition

The greater than symbol '>' is a mathematical operator that indicates a relationship where one value or quantity is larger than another. It is commonly used in the context of inequalities to represent a strict comparison between two numbers or expressions.

5 Must Know Facts For Your Next Test

1. The '>' symbol represents a strict comparison, meaning the value on the left side must be strictly greater than the value on the right side for the inequality to be true.
2. When solving linear inequalities, the direction of the inequality symbol (>, <, ≥, ≤) may change depending on the operations performed, such as multiplying or dividing both sides by a negative number.
3. Absolute value inequalities can be rewritten as the union of two linear inequalities, for example, $|x - 3| > 2$ can be written as $x - 3 > 2$ or $x - 3 < -2$.
4. The solution set for a linear inequality with the '>' symbol is represented by a half-plane on the coordinate plane, with the boundary line excluding the values that do not satisfy the inequality.
5. Graphing linear inequalities with the '>' symbol involves shading the appropriate half-plane, with the boundary line being excluded from the solution set.

Review Questions

• Explain how the '>' symbol is used in the context of linear inequalities and how it differs from the use of the '≥' symbol.
  • In the context of linear inequalities, the '>' symbol represents a strict comparison, meaning the value on the left side must be strictly greater than the value on the right side for the inequality to be true. This is in contrast to the '≥' symbol, which includes the possibility of the values being equal. When solving linear inequalities, the direction of the inequality symbol may change depending on the operations performed, such as multiplying or dividing both sides by a negative number. The solution set for a linear inequality with the '>' symbol is represented by a half-plane on the coordinate plane, with the boundary line excluding the values that do not satisfy the inequality.
• Describe the relationship between the '>' symbol and the concept of absolute value inequalities.
  • Absolute value inequalities can be rewritten as the union of two linear inequalities. For example, the inequality $|x - 3| > 2$ can be written as $x - 3 > 2$ or $x - 3 < -2$. In this case, the '>' symbol is used to represent the strict comparison between the absolute value of the expression and the constant on the right side of the inequality. The solution set for an absolute value inequality with the '>' symbol involves the union of the two half-planes that satisfy the corresponding linear inequalities.
• Analyze the role of the '>' symbol in the graphical representation of linear inequalities and how it differs from the graphical representation of absolute value inequalities.
  • When graphing linear inequalities with the '>' symbol, the solution set is represented by a half-plane on the coordinate plane, with the boundary line being excluded from the solution set. This is because the '>' symbol indicates a strict comparison, and the values on the boundary line do not satisfy the inequality. In contrast, the graphical representation of absolute value inequalities involves the union of two half-planes, as the absolute value inequality can be rewritten as the union of two linear inequalities. The boundary lines in the case of absolute value inequalities are included in the solution set, as they satisfy at least one of the corresponding linear inequalities.

Related terms

Inequality:

A mathematical statement that compares two quantities using operators such as >, <, ≥, or ≤, indicating that one value is greater than, less than, greater than or equal to, or less than or equal to the other.

Linear Inequality:

An inequality that can be written in the form $ax + b > 0$, where $a$ and $b$ are constants and $x$ is a variable.

Absolute Value Inequality:

An inequality that involves the absolute value of an expression, such as $|x - 3| > 2$, which represents the set of all values of $x$ for which the distance between $x$ and 3 is greater than 2.