In the realm of mathematics, inequalities play a crucial role in establishing relationships between variables. One such inequality, “if rt is greater than ba which statement is true,” presents an intriguing mathematical conundrum that we shall explore in this discourse.
By delving into the concepts of variables, mathematical symbols, and logical implications, we aim to unravel the truth behind this statement.
Throughout this analysis, we will define the variables rt and ba, elucidate the mathematical symbols “>” and “=”, and provide illustrative examples to enhance understanding. We will then embark on a journey to evaluate the condition “rt > ba,” employing methods for solving inequalities and delving into the concept of absolute values.
Subsequently, we will analyze the statement “if rt > ba,” examining its logical implications and identifying possible outcomes. To further solidify our understanding, we will construct a truth table and graph the inequality “rt > ba,” providing visual representations that aid in analyzing the statement.
Define the Variables rt and ba
In mathematics, rt and ba are variables that represent real numbers. They can take on any value, positive or negative, including zero.
Explain the Mathematical Symbols “>” and “=”
The mathematical symbol “>” means “greater than.” The symbol “=” means “equal to.” So, the expression “rt > ba” means that the value of rt is greater than the value of ba.
Provide Examples of Values for rt and ba
- If rt = 5 and ba = 2, then rt > ba because 5 is greater than 2.
- If rt = -3 and ba = -1, then rt > ba because -3 is greater than -1.
- If rt = 0 and ba = 0, then rt > ba is not true because 0 is not greater than 0.
Evaluate the Condition “rt > ba”
To determine if rt is greater than ba, we can use the following steps:
- Subtract ba from both sides of the inequality: rt
ba > 0.
- Solve the inequality rt
ba > 0 for rt.
The solution to the inequality rt – ba > 0 is rt > ba. Therefore, if rt – ba is positive, then rt is greater than ba.
Analyze the Statement “if rt > ba”
The statement “if rt > ba” is a logical implication. It means that if the condition rt > ba is true, then the conclusion is also true.
The possible outcomes when rt is greater than ba are:
- The conclusion is true.
- The conclusion is false.
The statement “if rt > ba” is true if and only if the conclusion is true when rt is greater than ba.
Construct a Truth Table
| rt | ba | if rt > ba |
|---|---|---|
| 5 | 2 | True |
| -3 | -1 | True |
| 0 | 0 | False |
The truth table shows that the statement “if rt > ba” is true when rt is greater than ba and false when rt is not greater than ba.
Graph the Inequality “rt > ba”: If Rt Is Greater Than Ba Which Statement Is True
The inequality rt > ba can be graphed on a Cartesian plane. The graph of the inequality is the set of all points (rt, ba) that satisfy the inequality.
The graph of the inequality rt > ba is a half-plane that is above the line ba = rt. The line ba = rt is the boundary of the half-plane.
FAQ Resource
What is the significance of the mathematical symbols “>” and “=”?
The symbol “>” represents “greater than,” indicating that one value is larger than another. The symbol “=” represents “equals,” indicating that two values are the same.
How do we determine if rt is greater than ba?
To determine if rt is greater than ba, we subtract ba from rt and check if the result is positive. If the result is positive, then rt is greater than ba.
What are the possible outcomes when rt is greater than ba?
When rt is greater than ba, the statement “if rt > ba” is true. This means that any statement that follows the “if” condition will also be true.
