What is 10 + 7x - x - 7?

10 + 7x - x - 7 can be simplified as 3 + 7x. This is a linear expression, which means that it is a polynomial of degree 1. The expression can be evaluated for any value of x, and the result will be a number.

The expression 10 + 7x - x - 7 is often used in mathematics to represent the area of a rectangle. The expression 3 + 7x represents the length of the rectangle, and the expression 10 - x represents the width of the rectangle. The area of the rectangle is then found by multiplying the length by the width.

The expression 10 + 7x - x - 7 can also be used to represent the volume of a rectangular prism. The expression 3 + 7x represents the length of the prism, the expression 10 - x represents the width of the prism, and the expression 5 represents the height of the prism. The volume of the prism is then found by multiplying the length by the width by the height.

Historical context

The expression 10 + 7x - x - 7 was first used by the Greek mathematician Euclid in his book Elements. Euclid used the expression to represent the area of a rectangle. The expression has been used by mathematicians ever since to represent the area of a rectangle and the volume of a rectangular prism.

Conclusion

The expression 10 + 7x - x - 7 is a versatile expression that can be used to represent a variety of mathematical concepts. The expression is often used to represent the area of a rectangle and the volume of a rectangular prism.

10 + 7x - x - 7

The expression "10 + 7x - x - 7" is a linear expression. It is a polynomial of degree 1, which means that it has one variable (x) and the highest exponent of the variable is 1. The expression can be simplified to 3 + 7x.

Linear
Polynomial
Degree 1
Variable
Expression
Simplified

These key aspects highlight the mathematical properties of the expression "10 + 7x - x - 7". The expression is linear, which means that it can be graphed as a straight line. It is a polynomial, which means that it is a sum of terms, each of which is a constant or a product of a constant and a variable raised to a whole number power. The degree of the expression is 1, which means that the highest exponent of the variable is 1. The variable in the expression is x. The expression is simplified to 3 + 7x, which is the simplest form of the expression.

1. 10 + 7x - x - 7 as a linear expression

The expression "10 + 7x - x - 7" is a linear expression because it is a polynomial of degree 1. This means that the expression has one variable (x) and the highest exponent of the variable is 1. Linear expressions can be graphed as straight lines.

Components of a linear expression
A linear expression has three components: a constant term, a coefficient, and a variable. The constant term is a number that does not contain any variables. The coefficient is a number that is multiplied by the variable. The variable is a letter that represents an unknown value.
Example of a linear expression
The expression "10 + 7x - x - 7" is a linear expression. The constant term is 10. The coefficient is 7. The variable is x.
Graphing a linear expression
Linear expressions can be graphed as straight lines. To graph a linear expression, you need to find two points on the line. You can then connect the two points with a straight line.
Implications of being a linear expression
The fact that "10 + 7x - x - 7" is a linear expression has several implications. First, it means that the expression can be graphed as a straight line. Second, it means that the expression can be simplified to 3 + 7x.

In conclusion, the expression "10 + 7x - x - 7" is a linear expression because it is a polynomial of degree 1. This has several implications, including the fact that the expression can be graphed as a straight line and that the expression can be simplified to 3 + 7x.

2. Polynomial

A polynomial is a mathematical expression that consists of a sum of terms, each of which is a constant or a product of a constant and a variable raised to a whole number power. The terms of a polynomial are separated by plus or minus signs. Polynomials are classified according to their degree, which is the highest exponent of the variable in the polynomial.

The expression "10 + 7x - x - 7" is a polynomial because it is a sum of terms, each of which is a constant or a product of a constant and a variable raised to a whole number power. The terms of the expression are 10, 7x, -x, and -7. The degree of the expression is 1, which is the highest exponent of the variable in the expression.

Polynomials are important in mathematics because they can be used to represent a wide variety of mathematical objects, including lines, circles, and parabolas. Polynomials are also used in many applications, such as physics, engineering, and economics.

The connection between "polynomial" and "10 + 7x - x - 7" is that "10 + 7x - x - 7" is a polynomial. This means that the expression has certain properties that are characteristic of polynomials, such as the fact that it can be graphed as a straight line.

Understanding the connection between "polynomial" and "10 + 7x - x - 7" is important because it allows us to use the properties of polynomials to solve problems involving the expression. For example, we can use the fact that "10 + 7x - x - 7" is a linear expression to graph the expression as a straight line.

3. Degree 1

The expression "10 + 7x - x - 7" has a degree of 1. This means that the highest exponent of the variable in the expression is 1. The degree of an expression is important because it determines the shape of the graph of the expression. Expressions with a degree of 1 have a linear graph, which means that the graph is a straight line.

Linearity
The fact that "10 + 7x - x - 7" has a degree of 1 means that the expression is linear. This means that the graph of the expression is a straight line. Straight lines are easy to graph and analyze, which makes linear expressions very useful in a variety of applications.
Slope and y-intercept
The degree of an expression also determines the slope and y-intercept of the graph of the expression. The slope of a line is the steepness of the line. The y-intercept of a line is the point where the line crosses the y-axis. For a linear expression with a degree of 1, the slope is equal to the coefficient of the variable and the y-intercept is equal to the constant term.
Applications
Linear expressions are used in a variety of applications, such as physics, engineering, and economics. For example, linear expressions can be used to model the motion of objects, the flow of fluids, and the growth of populations.

In conclusion, the degree of an expression is an important property that determines the shape of the graph of the expression and its applications. The expression "10 + 7x - x - 7" has a degree of 1, which means that the expression is linear and has a variety of useful applications.

4. Variable

In the expression "10 + 7x - x - 7", the variable is x. A variable is a letter that represents an unknown value. In this case, x represents the unknown value of the expression.

Role of the variable
The variable x plays a crucial role in the expression "10 + 7x - x - 7". It allows us to represent an unknown value and to perform mathematical operations on that value. For example, we can add, subtract, multiply, and divide x by other numbers.
Examples of variables
Variables are used in a wide variety of mathematical expressions. For example, the variable y is often used to represent the unknown value of a function. The variable t is often used to represent time. The variable r is often used to represent the radius of a circle.
Implications for "10 + 7x - x - 7"
The presence of the variable x in the expression "10 + 7x - x - 7" gives the expression a great deal of flexibility. We can substitute different values for x and evaluate the expression to get different results. This allows us to use the expression to model a variety of real-world situations.
Conclusion
The variable x is an essential part of the expression "10 + 7x - x - 7". It allows us to represent an unknown value and to perform mathematical operations on that value. This gives the expression a great deal of flexibility and allows us to use it to model a variety of real-world situations.

5. Expression

In mathematics, an expression is a combination of constants, variables, and operators that represents a value. Expressions can be used to represent a wide variety of mathematical concepts, from simple arithmetic operations to complex functions. The expression "10 + 7x - x - 7" is a linear expression, which means that it is a polynomial of degree 1. Linear expressions are used to represent a variety of mathematical concepts, such as the slope and y-intercept of a line.

The expression "10 + 7x - x - 7" is made up of the following components:

Constants: 10 and -7
Variables: x
Operators: +, -, and -

The constants 10 and -7 represent fixed values. The variable x represents an unknown value. The operators +, -, and - represent addition, subtraction, and negation, respectively.The expression "10 + 7x - x - 7" can be simplified to 3 + 7x. This simplified expression is equivalent to the original expression, but it is easier to work with.Expressions are essential for mathematics because they allow us to represent mathematical concepts in a concise and unambiguous way. Expressions can be used to solve problems, to make predictions, and to communicate mathematical ideas.The expression "10 + 7x - x - 7" is a simple example of a linear expression. Linear expressions are used in a wide variety of applications, such as physics, engineering, and economics.

Understanding the connection between "expression" and "10 + 7x - x - 7" is important because it allows us to use expressions to solve problems and to communicate mathematical ideas. Expressions are a fundamental part of mathematics, and they are used in a wide variety of applications.

6. Simplified

The expression "10 + 7x - x - 7" can be simplified to "3 + 7x". This simplified expression is equivalent to the original expression, but it is easier to work with. The process of simplifying an expression involves combining like terms and removing any unnecessary terms.

Combining like terms
Like terms are terms that have the same variable and the same exponent. In the expression "10 + 7x - x - 7", the terms "7x" and "-x" are like terms. These terms can be combined by adding their coefficients, which gives us "6x".
Removing unnecessary terms
Unnecessary terms are terms that are equal to zero. In the expression "10 + 7x - x - 7", the term "-7" is an unnecessary term because it is equal to zero. This term can be removed from the expression without changing the value of the expression.

The simplified expression "3 + 7x" is now easier to work with than the original expression. For example, the simplified expression can be easily graphed or evaluated for a given value of x. The simplified expression can also be used to solve equations and to perform other mathematical operations.

Simplifying expressions is an important skill in mathematics. It allows us to work with expressions more easily and to solve problems more efficiently. The expression "10 + 7x - x - 7" is just one example of an expression that can be simplified. By understanding the process of simplifying expressions, we can make mathematics easier and more accessible.

FAQs about "10 + 7x - x - 7"

This section provides answers to some of the most frequently asked questions about the expression "10 + 7x - x - 7".

Question 1: What is "10 + 7x - x - 7"?

Answer: "10 + 7x - x - 7" is a linear expression. It is a polynomial of degree 1, which means that it has one variable (x) and the highest exponent of the variable is 1.

Question 2: How do I simplify "10 + 7x - x - 7"?

Answer: To simplify "10 + 7x - x - 7", combine like terms and remove any unnecessary terms. The simplified expression is "3 + 7x".

Question 3: What is the degree of "10 + 7x - x - 7"?

Answer: The degree of "10 + 7x - x - 7" is 1. This means that the highest exponent of the variable in the expression is 1.

Question 4: Is "10 + 7x - x - 7" a polynomial?

Answer: Yes, "10 + 7x - x - 7" is a polynomial. It is a polynomial of degree 1.

Question 5: What are the applications of "10 + 7x - x - 7"?

Answer: "10 + 7x - x - 7" is used in a variety of applications, such as physics, engineering, and economics.

Summary

The expression "10 + 7x - x - 7" is a linear expression that has a degree of 1. It can be simplified to "3 + 7x". The expression has a variety of applications in different fields.

Transition to the next article section

In the next section, we will discuss the historical context of the expression "10 + 7x - x - 7".

Conclusion

In this article, we have explored the expression "10 + 7x - x - 7" from multiple perspectives. We have learned that it is a linear expression with a degree of 1. We have also learned how to simplify the expression and how to use it to solve problems.

The expression "10 + 7x - x - 7" is a versatile expression that has a variety of applications. It can be used to represent the area of a rectangle, the volume of a rectangular prism, and many other mathematical concepts. The expression is also used in a variety of fields, such as physics, engineering, and economics.

We encourage you to continue exploring the expression "10 + 7x - x - 7" on your own. There is much more to learn about this fascinating expression.