Simplify this expression: [tex]$4 p+9+(-7 p)+2$[/tex]
A. [tex]$3 p+11$[/tex]
B. [tex]$-3 p+11$[/tex]
C. [tex]$11 p+11$[/tex]
D. [tex]$3 p+7$[/tex]
Answer (2)
Group like terms: 4 p + ( − 7 p ) + 9 + 2 .
Combine 'p' terms: 4 p − 7 p = − 3 p .
Combine constant terms: 9 + 2 = 11 .
The simplified expression is − 3 p + 11 .
Explanation
Understanding the Problem We are asked to simplify the expression 4 p + 9 + ( − 7 p ) + 2 and choose the correct simplified form from the given options.
Identifying Like Terms To simplify the expression, we need to combine the like terms. Like terms are terms that have the same variable raised to the same power. In this expression, the like terms are the terms with the variable p and the constant terms.
Grouping Like Terms First, let's group the like terms together: 4 p + ( − 7 p ) + 9 + 2 .
Combining 'p' Terms Now, let's combine the terms with the variable p : 4 p + ( − 7 p ) = ( 4 − 7 ) p = − 3 p .
Combining Constant Terms Next, let's combine the constant terms: 9 + 2 = 11 .
Final Simplified Expression So, the simplified expression is − 3 p + 11 . Comparing this with the given options, we see that option B matches our simplified expression.
Examples
Simplifying expressions is a fundamental skill in algebra. For example, if you are buying items at a store, you can use this skill to calculate the total cost. Suppose you buy 4 apples that cost 'p' dollars each, and you have a coupon for a $9 discount, but there's also a $2 tax. The total cost can be represented as 4 p + 9 + 2 . Simplifying this expression helps you quickly determine the final amount you need to pay.
The simplified expression for 4 p + 9 + ( − 7 p ) + 2 is − 3 p + 11 , which corresponds to option B. Hence, the answer chosen is B. This process involves combining like terms carefully to arrive at the final simplified expression.
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