Simplify this expression: [tex]4 \rho+9+(-7 p)+2[/tex]
A) [tex]3 p+7[/tex]
B) [tex]11 p+11[/tex]
C) [tex]3 p+11[/tex]
D) [tex]-3 p+11[/tex]
Answer (1)
We simplify the expression 4 ρ + 9 + ( − 7 p ) + 2 by combining like terms. Assuming ρ is a typo and should be p , we combine the p terms and the constant terms. This gives us:
Combine 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 Expression We are asked to simplify the expression 4 h o w + 9 + ( − 7 p ) + 2 . This involves combining like terms, which are the constant terms and the terms with the same variable.
Grouping Like Terms First, let's rewrite the expression to group the like terms together: 4 h o w + 9 + ( − 7 p ) + 2 = 4 h o w − 7 p + 9 + 2
Combining Constants Now, we combine the constant terms: 9 + 2 = 11 So the expression becomes: 4 h o w − 7 p + 11
Simplifying with the Typo Assumption If we assume that ρ is a typo and it should be p , then the expression becomes: 4 p − 7 p + 11 Combining the p terms: 4 p − 7 p = − 3 p So the simplified expression is: − 3 p + 11
Matching the Options Comparing our simplified expression − 3 p + 11 with the given options, we see that it matches option D.
Examples
Simplifying expressions is a fundamental skill in algebra and is used in many real-world applications. For example, if you are calculating the total cost of items with discounts and taxes, you need to combine like terms to find the final price. Suppose you have 4 items each costing 'p' dollars, but there's a discount of 7 dollars on each of these items, and an additional fixed cost of 11 dollars for shipping. The total cost can be represented as 4 p − 7 p + 11 , which simplifies to − 3 p + 11 . This shows how simplifying algebraic expressions can help in everyday financial calculations.
