Verified Answer :

  • Identify the constant terms \(6\) and \(7\) in the expression \(8q + 6 + 7\).
  • Add the constants together: \(6 + 7 = 13\).
  • Combine the result with the variable term \(8q\) to obtain the final simplified expression \(\boxed{8q + 13}\).

Explanation

  1. Analyzing the Expression

The expression provided is \(8q + 6 + 7\). To simplify this, we identify the like terms. In algebra, like terms are terms that contain the same variables raised to the same powers, or in this case, constant numerical values. Here, the variable term is \(8q\), and the constant terms are \(6\) and \(7\). Constants can be added together directly to simplify an expression.

  1. Combining Like Terms

To combine the like terms, we add the constant numbers \(6\) and \(7\):
\[6 + 7 = 13\]
After adding these, we keep the variable term \(8q\) as it is, because there are no other terms with the variable \(q\) to combine it with. Thus, the simplified expression becomes \(8q + 13\).

Examples

Suppose you are managing a small inventory of notebooks. You have 8 packs of notebooks, where each pack contains \(q\) notebooks, plus 6 single notebooks you bought yesterday and 7 more that were donated today. To find the total number of notebooks you have, you group the packs together and add up the single notebooks: \(8q + (6 + 7) = 8q + 13\). Combining like terms is a essential skill for organizing and calculating quantities efficiently in everyday life.

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