Question

Identify the terms of the algebraic expression.\(-5+3 x\)

Short answer

The terms of the given algebraic expression \(-5+3x\) are \(-5\) and \(3x\).

Step-by-step solution

Identify the terms

Scan through the algebraic expression \(-5+3x\) and identify the parts separated by '+' or '-' signs. Here, there are two such parts. First, there is \(-5\), which is a constant term (a term without a variable), and then there is \(3x\), which is a variable term (a term that includes a variable).

Conclusion

After breaking down the expression, the terms for the expression \(-5+3x\) can be identified as \(-5\) and \(3x\).

Key concepts

Constant Term

Understanding the constant term in an algebraic expression is crucial for mastering algebra. A constant term is a value that does not change; it stands alone without any variables attached to it. This means it is not affected by the values of the variables in an expression. For example, in the expression \( -5+3x \), \( -5 \) is considered a constant term because it is independent of the variable \( x \) and maintains its value regardless of \( x \) changing.

Constant terms are the solid ground amidst the shifting parts of an equation. They play a key role in algebraic operations, such as simplifying expressions and solving equations, and often represent a starting value or a shift along the number line. In practical scenarios, constant terms can represent fixed costs, start-up values, or other unchanging quantities in real-world problems.

Variable Term

In contrast to constant terms, variable terms are the dynamic part of an algebraic expression. A variable term includes both a number, known as the coefficient, and a variable, which represents an unknown or changeable quantity. For instance, looking at the expression \( -5+3x \), we notice \( 3x \) as the variable term. Here, \( 3 \) is the coefficient that multiplies the variable \( x \).

The variable term is where the action happens in algebra. It represents quantities that can change or vary, and it's through the manipulation of these terms that algebraic problems are often solved. Variable terms can model a wide array of real-world situations, like the rate of change, growth or decay over time, or relationships between different quantifiable concepts.

Identifying Terms in Algebra

Identifying terms in an algebraic expression is a foundational skill in algebra. Terms are essentially the building blocks of algebraic expressions, separated by addition or subtraction signs. When analyzing the expression \( -5+3x \), there are two distinct terms: the constant term \( -5 \) and the variable term \( 3x \).

To effectively identify these terms, look for the plus \( + \) and minus \( - \) signs that separate them. Each term can either be a constant or a variable term, which can further contain coefficients and exponents. Mastery of this step allows for deeper understanding of more complex operations like simplifying expressions, distributing terms, combining like terms, or solving equations.