Introducing the expression “four times a number decreased by six,” this discourse embarks on a journey to unravel its mathematical intricacies. Through a comprehensive examination, we delve into the depths of this expression, exploring its simplification, evaluation, and practical applications, while uncovering its interconnectedness with broader mathematical concepts.
Unveiling the essence of this expression, we embark on a step-by-step analysis, elucidating its algebraic representation and unraveling the intricacies of its simplification process. With precision and clarity, we demonstrate how algebraic operations transform the expression, revealing its underlying structure.
Defining the Expression
The expression “four times a number decreased by six” can be interpreted as a mathematical operation that involves a variable, represented by the word “number,” and two constants, “four” and “six.”
In algebraic terms, the expression can be represented as 4x – 6, where x represents the unknown number.
Expression Interpretation
- The phrase “four times a number” indicates that the unknown number is multiplied by four.
- The phrase “decreased by six” suggests that the result of the multiplication is then reduced by six.
Therefore, the expression 4x – 6 represents the mathematical operation of multiplying an unknown number by four and then subtracting six from the product.
Simplifying the Expression
Simplifying an expression involves manipulating the expression using algebraic operations to make it easier to understand and work with.
The expression “four times a number decreased by six” can be written as 4x – 6, where x represents the number.
Simplifying 4x
6
6
To simplify the expression 4x – 6, we can use the following steps:
- Distribute the 4 to the terms inside the parentheses:
- 6 = 4x
- 4(1) = 4x
- 4
- Combine like terms:
- 4 = 4x
- 4 = 4x
- 4 = 0
4x
4x
Therefore, the simplified expression is 0.
Evaluating the Expression: Four Times A Number Decreased By Six
To evaluate the expression “four times a number decreased by six,” we need to substitute the number with a specific value and perform the operations indicated in the expression.
For example, if the number is 5, the expression becomes:
4
- 5
- 6 = 14
Therefore, when the number is 5, the expression evaluates to 14.
Substituting Different Values
We can evaluate the expression for different values of the number to obtain different results:
- If the number is 10, the expression becomes: 4 – 10 – 6 = 34
- If the number is -2, the expression becomes: 4 – (-2) – 6 = -14
- If the number is 0, the expression becomes: 4 – 0 – 6 = -6
Applications of the Expression
The expression “four times a number decreased by six” can be applied in various real-world scenarios. It finds practical use in fields such as economics, finance, physics, and engineering, where mathematical modeling and problem-solving are essential.
For instance, in economics, the expression can be used to represent the relationship between the price of a product and its demand. The number can represent the price, and the expression “four times a number decreased by six” can represent the demand.
By analyzing this expression, economists can predict how changes in price affect demand and make informed decisions about pricing strategies.
Example: Calculating Distance
In physics, the expression can be used to calculate the distance traveled by an object moving at a constant speed. The number can represent the speed, and the expression “four times a number decreased by six” can represent the distance traveled.
By plugging in the speed and the time, we can determine the distance traveled by the object.
Example: Determining Revenue
In finance, the expression can be used to determine the revenue generated by a company. The number can represent the number of units sold, and the expression “four times a number decreased by six” can represent the revenue generated. By multiplying the number of units sold by the price per unit (which is represented by four times the number decreased by six), we can calculate the total revenue earned by the company.
Related Concepts
The expression “four times a number decreased by six” is related to several mathematical concepts, including:
These concepts can be used to analyze and understand the expression in various ways.
Linear Expressions, Four times a number decreased by six
The expression “four times a number decreased by six” is a linear expression. A linear expression is an algebraic expression that contains only one variable and has no exponents greater than one.
Linear expressions can be used to represent a wide variety of real-world situations, such as the cost of a product, the distance traveled by a car, or the area of a rectangle.
Slope and Intercept
The slope and intercept of a linear expression are two important properties that can be used to analyze the expression.
The slope of a linear expression is the coefficient of the variable. The intercept of a linear expression is the constant term.
The slope and intercept of a linear expression can be used to graph the expression and to determine its key features, such as the x-intercept and the y-intercept.
Linear Equations
A linear equation is an equation that can be written in the form y = mx + b, where mis the slope and bis the intercept.
Linear equations can be used to solve a variety of problems, such as finding the value of a variable or determining the relationship between two variables.
Applications of Linear Expressions
Linear expressions have a wide variety of applications in real-world situations.
For example, linear expressions can be used to:
- Calculate the cost of a product
- Determine the distance traveled by a car
- Find the area of a rectangle
- Solve a variety of other problems
FAQ Resource
What is the algebraic representation of “four times a number decreased by six”?
The algebraic representation is 4x – 6, where x represents the unknown number.
How do you simplify the expression “four times a number decreased by six”?
Simplify by performing the multiplication operation first, and then the subtraction operation. The simplified expression is 4x – 6.
What are some real-world applications of the expression “four times a number decreased by six”?
One application is calculating the total cost of purchasing a certain number of items when each item costs a specific amount and there is a discount or reduction in price.
