Simplify: $b+7+b-2$
A. 7
B. $-7+9 b$
C. $-6 b$
D. $2 b+5$
Answer (2)
Combine the 'b' terms: b + b = 2 b .
Combine the constant terms: 7 − 2 = 5 .
Write the simplified expression as the sum of the combined terms: 2 b + 5 .
The simplified expression is 2 b + 5 .
Explanation
Understanding the Problem We are given the expression b + 7 + b − 2 . Our goal is to simplify it by combining like terms.
Identifying Like Terms First, let's identify the like terms in the expression. We have two 'b' terms and two constant terms.
Combining 'b' Terms Now, let's combine the 'b' terms: b + b = 2 b .
Combining Constant Terms Next, let's combine the constant terms: 7 − 2 = 5 .
Writing the Simplified Expression Finally, let's write the simplified expression as the sum of the combined terms: 2 b + 5 .
Final Answer Therefore, the simplified expression is 2 b + 5 . Looking at the multiple-choice options, we see that option D matches our simplified expression.
Examples
Simplifying expressions is a fundamental skill in algebra, and it's used in many real-world situations. For example, imagine you're buying ingredients for a recipe. You need 'b' amount of flour and 'b' amount of sugar, plus 7 apples and you already have 2 apples at home. The expression b+7+b-2 helps you determine the total amount of ingredients you need to buy: 2b + 5. This skill is also useful in budgeting, calculating distances, and many other everyday tasks.
The simplified expression of b + 7 + b − 2 is 2 b + 5 . Therefore, the correct answer is option D: 2 b + 5 . This result comes from combining like terms in the expression.
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