Which expression is equivalent to 1/3b-7 – Exploring the mathematical landscape, we embark on a journey to unravel the enigmatic expression “1/3b-7.” Delving into the intricacies of algebraic operations, we will uncover the secrets hidden within this enigmatic equation, revealing its true nature and uncovering its equivalent forms.
Through a meticulous exploration of mathematical principles and real-world applications, we will shed light on the significance of this expression, empowering you with a deeper understanding of its practical implications.
1. Understand the Expression: Which Expression Is Equivalent To 1/3b-7
The expression “1/3b-7” involves the mathematical operations of division and subtraction. It can be broken down into its component parts as follows:
- 1/3b: This represents the quotient of 1 divided by 3b, where b is a variable.
- -7: This is a constant value that is subtracted from the result of 1/3b.
To understand the concept, consider the following examples:
- If b = 3, then 1/3b-7 = 1/3(3) – 7 = 1/9 – 7 = -63/9 = -7.
- If b = -2, then 1/3b-7 = 1/3(-2) – 7 = -1/6 – 7 = -13/6.
2. Simplify the Expression
To simplify the expression “1/3b-7”, we can apply the following steps:
- Factor out 1/3 from the expression: 1/3(b-21).
- Simplify the expression within the parentheses: b-21.
Therefore, the simplified expression is 1/3(b-21).
3. Identify Equivalent Expressions
Expressions that have the same value for all values of the variable are considered equivalent. To find equivalent expressions for “1/3b-7”, we can use the following algebraic methods:
- Adding a constant:Adding the same constant to both sides of the expression results in an equivalent expression. For example, 1/3b-7 + 7 = 1/3b.
- Multiplying by a constant:Multiplying both sides of the expression by the same non-zero constant results in an equivalent expression. For example, 3(1/3b-7) = b-21.
The following table summarizes the equivalent expressions and their corresponding transformations:
| Expression | Transformation |
|---|---|
| 1/3b-7 | Original expression |
| 1/3b | Add 7 to both sides |
| b-21 | Multiply both sides by 3 |
4. Applications and Examples
The expression “1/3b-7” or its equivalent forms may be applied in various real-world scenarios:
- Calculating the average:In statistics, the average of a set of numbers can be calculated using the formula 1/n(Σx – nμ), where n is the number of values, Σx is the sum of the values, and μ is the mean of the values.
This formula is equivalent to 1/3b-7 if n = 3 and μ = 7.
- Solving equations:The expression 1/3b-7 can be used to solve equations involving linear functions. For example, to solve the equation 1/3b-7 = 5, we can add 7 to both sides and then multiply both sides by 3 to get b = 36.
Detailed FAQs
What is the significance of the expression “1/3b-7”?
The expression “1/3b-7” represents a mathematical operation involving division and subtraction. Understanding its mathematical operations and equivalent forms is crucial for solving equations and applying it in various mathematical contexts.
How can I simplify the expression “1/3b-7”?
To simplify “1/3b-7,” apply the distributive property and combine like terms. The simplified form may vary depending on the specific values of b and the context in which the expression is used.
What are some real-world applications of the expression “1/3b-7”?
The expression “1/3b-7” finds applications in various fields, including physics, engineering, and economics. For instance, it can be used to calculate the average speed of an object or determine the slope of a line.
