Inequality Symbols

Definition

Inequality symbols are mathematical notations used to represent relationships between two quantities or expressions where one is greater than, less than, or not equal to the other. These symbols are essential in solving linear and compound inequalities.

5 Must Know Facts For Your Next Test

1. Inequality symbols are used to represent relationships between two expressions, such as $x > 5$ or $y \leq 3$.
2. The direction of the inequality symbol (greater than, less than, or not equal to) indicates the relationship between the two values or expressions.
3. Solving linear inequalities involves finding the set of values for a variable that satisfy the given inequality.
4. Compound inequalities involve the use of two or more inequality symbols, such as $-2 \leq x < 5$, which represents a range of values for the variable.
5. The properties of inequality symbols, such as the transitive property and the multiplication/division property, are essential in solving and manipulating inequalities.

Review Questions

• Explain the difference between the greater than (>) and greater than or equal to (≥) inequality symbols, and provide examples of how they are used in solving linear inequalities.
  • The greater than (>) symbol indicates that one value is strictly larger than another, while the greater than or equal to (≥) symbol indicates that one value is either larger than or equal to another. For example, the inequality $x > 5$ means that the variable $x$ must be a value greater than 5, while the inequality $x \geq 5$ includes values that are equal to 5 as well as those greater than 5. The choice of which symbol to use depends on the specific requirements of the problem being solved.
• Describe how to solve a compound inequality, such as $-2 \leq x < 5$, and explain the significance of the two inequality symbols in this type of expression.
  • To solve a compound inequality, you need to consider the relationship between the two inequality symbols. In the expression $-2 \leq x < 5$, the first inequality symbol (\leq) indicates that the variable $x$ must be greater than or equal to -2, while the second inequality symbol (<) indicates that $x$ must be less than 5. The solution to this compound inequality is the set of values for $x$ that satisfy both inequalities, which in this case would be the range $-2 \leq x < 5$. Compound inequalities are useful in representing and solving problems that involve a range of acceptable values for a variable.
• Analyze the role of inequality symbols in the context of solving and graphing linear inequalities, and explain how the properties of these symbols, such as the transitive property, can be used to manipulate and simplify inequalities.
  • Inequality symbols are fundamental in solving and graphing linear inequalities. The transitive property of inequality symbols, which states that if $a > b$ and $b > c$, then $a > c$, allows you to simplify and manipulate inequalities. For example, if you have the inequality $2x + 3 > 5$, you can subtract 3 from both sides to get $2x > 2$, and then divide both sides by 2 to get $x > 1$. The properties of inequality symbols, such as the transitive property and the multiplication/division property, enable you to perform algebraic operations on inequalities and find the set of values that satisfy the given conditions. Understanding how to use and apply these properties is crucial in solving a variety of linear inequality problems.

Related terms

Greater Than (>): The symbol used to indicate that one value is numerically larger than another.

Less Than (<): The symbol used to indicate that one value is numerically smaller than another.

Not Equal To (≠): The symbol used to indicate that two values are not the same or do not represent the same quantity.