Problem 3 - Prealgebra

Question

Identify the terms, like terms, coefficients, and constants in expression. \(4 y-2 x-7\)

Step-by-Step Solution

Answer

The terms are \(4y\), \(-2x\), and \(-7\). Coefficients are 4 and -2. The constant is -7. No like terms exist.

Step 1: Identify the Terms

In the expression, the terms are the parts of the expression that are added or subtracted. Look at each separate part. The expression is written as \(4y - 2x - 7\). The terms are \(4y\), \(-2x\), and \(-7\).

Step 2: Identify the Coefficients

The coefficient is a number that is multiplied by a variable in a term. For \(4y\), the coefficient is 4. For \(-2x\), the coefficient is -2. Constants do not have coefficients because they do not have variables.

Step 3: Identify the Constants

In the expression, a constant is a term that does not have a variable. In the expression \(4y - 2x - 7\), the constant is \(-7\). It doesn't change regardless of the values of \(x\) or \(y\).

Step 4: Find Like Terms

Like terms are terms that contain the same variables raised to the same power. In the expression \(4y - 2x - 7\), there are no like terms present because the variables \(y\) and \(x\) are different.

Key Concepts

Expressions

An expression in mathematics is a combination of numbers, variables, and mathematical operations like addition, subtraction, multiplication, and division. Expressions don't have an equal sign, which distinguishes them from equations.
For example, the expression \(4y - 2x - 7\) is made up of numbers, variables \(x\) and \(y\), and operations like subtraction. Understanding the parts of an expression is crucial in solving and simplifying them.

Terms

Terms are the different parts of an expression that are separated by the plus \((+)\) or minus \((-1)\) signs. Each term can be a number, a variable, or a combination of both.
In the expression \(4y - 2x - 7\), there are three terms:

• \(4y\)
• \(-2x\)
• \(-7\)

Think of terms as individual members of the expression family, each playing its unique role. Identifying them helps in further analysis like factoring or simplifying expressions.

Coefficients

Coefficients are the numerical part of the terms in an expression that have variables. They show how many times a term is multiplied by the variable.
In the expression \(4y - 2x - 7\):

• For the term \(4y\), the coefficient is \(4\).
• For the term \(-2x\), the coefficient is \(-2\).

Coefficients help in understanding the weight or importance of each variable in the expression. Once you identify the coefficients, you can easily rewrite the expression to simplify or expand it depending on the requirements.

Constants

Constants in an algebraic expression are numbers that do not have any variables attached to them. They remain unchanged regardless of the input values of the variables.
In \(4y - 2x - 7\), the constant is \(-7\). Constants are important because they represent fixed values in problems, providing a stable anchor around which the rest of the variables may fluctuate. Recognizing constants is crucial when simplifying expressions or when solving equations since they can influence the overall outcome.