Simplify this expression: [tex]$4 p+9+(-7 p)+2$[/tex]
A) [tex]$-3 p+11$[/tex]
B) [tex]$3 p+7$[/tex]
C) [tex]$3 p+11$[/tex]
D) [tex]$11 p+11$[/tex]
Answer (1)
Combine the 'p' terms: 4 p + ( − 7 p ) = − 3 p .
Combine the constant terms: 9 + 2 = 11 .
Write the simplified expression: − 3 p + 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 . This involves combining like terms, which are the terms with the variable p and the constant terms.
Combining 'p' terms First, 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
Simplified Expression Now, we combine the results to get the simplified expression: − 3 p + 11
Final Answer Therefore, the simplified expression is − 3 p + 11 . Comparing this to the given options, we see that it matches option A.
Examples
Simplifying expressions is a fundamental skill in algebra and is used in many real-world applications. For example, suppose you are buying items at a store. You want to buy 4 apples and 9 bananas, but the store has a promotion where you get 7 apples for free if you buy a certain amount of other fruit. Also, you have a coupon for 2 extra bananas. If we let p represent the price of an apple, then the total cost can be represented as 4 p + 9 + ( − 7 p ) + 2 . Simplifying this expression to − 3 p + 11 helps you understand the actual cost depending on the price of the apples.
