Verified Answer :

  • Algebraic terms are components separated by addition or subtraction operators.
  • The expression \(2n + 5 - 3p + 4q\) contains four distinct components: \(2n\), \(5\), \(3p\), and \(4q\).
  • By counting these components, we find there are 4 terms in the expression.
  • The correct answer is \(\boxed{4}\).

Explanation

  1. Understanding Algebraic Terms

To determine the number of terms in an algebraic expression, we first identify its definition. In algebra, terms are the parts of an expression that are separated by addition (\(+\)) or subtraction (\(-\)) signs. Each term is an individual component that can be a number, a variable, or a product of numbers and variables.

  1. Identifying the Terms

The given expression is \(2n + 5 - 3p + 4q\). We can see the components separated by the operators:

  1. The first component is \(2n\).
  2. The next component is \(5\), separated from \(2n\) by a \(+\) sign.
  3. The third component is \(3p\), separated from \(5\) by a \(-\) sign.
  4. The final component is \(4q\), separated from \(3p\) by a \(+\) sign.

Thus, the expression is composed of the four distinct parts: \(2n\), \(5\), \(3p\), and \(4q\).

  1. Counting the Terms

Counting the components identified in the previous step, we have:

  • Term 1: \(2n\)
  • Term 2: \(5\)
  • Term 3: \(3p\)
  • Term 4: \(4q\)

There are 4 terms in the expression. The correct choice is 4.

Examples

Understanding how to identify and count terms is a fundamental skill in algebra, similar to organizing items in a grocery list or inventory. For example, if a company calculates its daily budget using the formula Revenue + Savings - Expenses - Taxes, identifying these distinct parts helps in managing finances effectively. Just like the algebraic expression, knowing the number of components allows for better categorization and analysis of complex systems in real-world budgeting and planning.

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