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Definition

The less than symbol, <, is a mathematical operator that indicates a relationship where one value is smaller than another value. It is used in various contexts within algebra to represent inequalities, where the solution set includes all values that satisfy the inequality condition.

5 Must Know Facts For Your Next Test

1. The less than symbol, <, is used to represent a strict inequality, where the solution set includes all values that are strictly less than the given value.
2. When solving linear inequalities, the properties of inequality are used to isolate the variable and find the solution set.
3. Compound inequalities involve the use of the less than symbol, <, along with the greater than symbol, >, to represent a range of values.
4. Graphing linear inequalities in two variables involves shading the appropriate half-plane based on the direction of the inequality.
5. Solving rational inequalities and quadratic inequalities often involves the use of the less than symbol, <, to represent the solution set.

Review Questions

• Explain how the less than symbol, <, is used in the context of solving linear inequalities.
  • When solving linear inequalities, the less than symbol, <, is used to represent a strict inequality. This means that the solution set includes all values that are strictly less than the given value. To solve a linear inequality, you would use the properties of inequality to isolate the variable and find the range of values that satisfy the inequality condition. For example, to solve the inequality $3x - 5 < 11$, you would add 5 to both sides to get $3x < 16$, and then divide both sides by 3 to get $x < \frac{16}{3}$.
• Describe how the less than symbol, <, is used in the context of graphing linear inequalities in two variables.
  • When graphing linear inequalities in two variables, the less than symbol, <, is used to indicate the direction of the inequality. Specifically, the less than symbol, <, corresponds to shading the half-plane that is below the line representing the inequality. For example, to graph the inequality $2x + 3y < 12$, you would first plot the line $2x + 3y = 12$, and then shade the half-plane that is below this line, as this represents the solution set for the inequality.
• Analyze the role of the less than symbol, <, in the context of solving rational inequalities and quadratic inequalities.
  • In the context of solving rational inequalities and quadratic inequalities, the less than symbol, <, is used to represent the solution set. For rational inequalities, the less than symbol may be used to indicate the range of values for the variable that satisfy the inequality condition. For example, to solve the inequality $\frac{x + 2}{x - 1} < 3$, you would need to consider the values of $x$ that make the expression less than 3. Similarly, in the context of solving quadratic inequalities, the less than symbol, <, is used to represent the range of values for the variable that satisfy the inequality condition. For instance, to solve the inequality $x^2 - 4x + 3 < 0$, you would need to find the values of $x$ that make the expression less than 0.

Related terms

Inequality:

A mathematical statement that shows a relationship between two expressions where one is greater than, less than, or not equal to the other.

Linear Inequality:

An inequality that can be written in the form $ax + b < c$, where $a$, $b$, and $c$ are real numbers and $x$ is a variable.

Compound Inequality:

An inequality that consists of two or more individual inequalities combined using the words 'and' or 'or'.