Problem 83 - Algebra 1: Concepts and Skills

Question

Identify the terms of the expression. \(-7 x+4 x\)

Step-by-Step Solution

Answer

The terms of the expression \(-7 x+4 x\) are -7x and 4x.

Step 1: Identify the first term

The first term of the expression is -7x. It is a term because it is composed by a number and a variable multiplied together.

Step 2: Identify the second term

The second term is 4x. Similarly to the first term, it consists of a number and a variable multiplied together.

Key Concepts

Terms of an Expression

Understanding algebra begins with the basic building block known as an algebraic expression. An expression is a combination of numbers, variables, and operators (like + and -) that represents a value. Within an expression, we have 'terms,' which are parts of the expression separated by a plus (+) or minus (-) sign.

For instance, in the expression \( -7x + 4x \), we have two distinct terms: \( -7x \) and \( 4x \). Each term is a product of a number (known as the coefficient) and a variable. The first term, \( -7x \), has a coefficient of -7 reflecting its value and sign, while the second term, \( 4x \), has a coefficient of 4. Understanding terms is essential, as it lays the groundwork for further operations in algebra, such as simplification and solving equations.

Variables in Algebra

In algebra, variables are symbols that represent unknown values and can take on different numerical values. They are typically denoted by letters such as x, y, and z. In the given expression \( -7x + 4x \), 'x' is the variable, and it's crucial for understanding the behavior of algebraic expressions over various values.

The use of variables allows for generalization in algebra, enabling one to create formulas and equations applicable in numerous instances, rather than just for specific numbers. When dealing with variables, always pay attention to their coefficients and the operations applied to them, as this will influence the final outcome when values are substituted for the variables.

Combining Like Terms

Algebra often involves simplifying expressions to make them easier to work with. One key simplification process is 'combining like terms.' Like terms are terms within an expression that have exactly the same variable parts, meaning they have the same variable(s) raised to the same power. In our example, \( -7x \) and \( 4x \) are like terms because they both contain the variable 'x' with no exponent, or to the first power by default.

To combine like terms, simply add or subtract their coefficients. For \( -7x + 4x \), we combine the coefficients -7 and 4, resulting in \( -3x \), which is the simplified version of the given expression. This step condenses the expression and makes it clearer and less complex, which is especially helpful when tackling more intricate algebraic problems.