An inequality is an equation that contains symbols like <, >.
Understand the Problem
The question is defining what an inequality is, indicating that it involves comparison symbols such as less than (<) and greater than (>). It seeks clarification on the concept of inequalities in mathematics.
Answer
An inequality is a mathematical expression comparing two values using symbols like $<$ and $>$.
Answer for screen readers
An inequality is a mathematical statement that compares two values using symbols such as less than ($<$) or greater than ($>$).
Steps to Solve
- Define an Inequality
An inequality is a mathematical expression that describes the relationship between two values, indicating how one value compares to another. It uses symbols such as less than ($<$), greater than ($>$), less than or equal to ($\leq$), and greater than or equal to ($\geq$).
- Use of Comparison Symbols
The comparison symbols in inequalities represent the following:
- The symbol $<$ means "less than."
- The symbol $>$ means "greater than."
- The symbol $\leq$ means "less than or equal to."
- The symbol $\geq$ means "greater than or equal to."
- Examples of Inequalities
Inequalities can be expressed in various forms. Here are a few examples:
- $3 < 5$ means 3 is less than 5.
- $7 \geq 4$ means 7 is greater than or equal to 4.
- $x < 10$ indicates that any value of $x$ must be less than 10.
- Graphing Inequalities
Inequalities can also be represented on a number line. For example:
- The inequality $x < 3$ can be graphed as an open circle at 3, indicating that 3 is not included, and a line extending to the left.
- The inequality $x \geq 2$ can be graphed with a closed circle at 2, indicating that 2 is included, and a line extending to the right.
An inequality is a mathematical statement that compares two values using symbols such as less than ($<$) or greater than ($>$).
More Information
Inequalities are fundamental in mathematics as they help describe ranges of values and are used widely in fields like algebra, calculus, and economics. They can represent real-world situations, such as economic constraints, and are essential for solving equations that have multiple solutions.
Tips
- Confusing the symbols: It's important to remember what each symbol stands for. Make sure to review the definitions of $<$, $>$, $\leq$, and $\geq$ to avoid errors.
- Misinterpreting the graph: When graphing inequalities, ensure to use open circles for greater-than/less-than and closed circles for greater-than-or-equal/less-than-or-equal.
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