Which expression is equivalent to [tex]$10 k+17-7 j-18-11 k$[/tex]?
A. [tex]$-8 j k-1$[/tex]
B. [tex]$-7 j-k-1$[/tex]
C. [tex]$-7 j+k+1$[/tex]
D. [tex]$-8 j-k$[/tex]
Answer (2)
Combine the k terms: 10 k − 11 k = − k .
Combine the constant terms: 17 − 18 = − 1 .
Rewrite the expression: − k − 7 j − 1 = − 7 j − k − 1 .
The equivalent expression is − 7 j − k − 1 .
Explanation
Understanding the Problem We are given the expression 10 k + 17 − 7 j − 18 − 11 k and asked to find an equivalent expression from the given options. To do this, we need to combine like terms.
Grouping Like Terms First, let's group the like terms together: ( 10 k − 11 k ) + ( − 7 j ) + ( 17 − 18 ) .
Combining k Terms Now, combine the k terms: 10 k − 11 k = − 1 k = − k .
Combining Constant Terms Next, combine the constant terms: 17 − 18 = − 1 .
Simplified Expression So, the simplified expression is − k − 7 j − 1 , which can be rewritten as − 7 j − k − 1 .
Finding the Equivalent Expression Comparing this with the given options, we see that the equivalent expression is − 7 j − k − 1 .
Examples
Understanding how to simplify algebraic expressions by combining like terms is a fundamental skill in algebra. This skill is used in many real-world applications, such as calculating costs, determining distances, and modeling various phenomena in physics and engineering. 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 amount. Suppose you buy 10 apples at k dollars each, get a discount of 17 dollars, pay a tax of 7 j dollars, get another discount of 18 dollars, and buy 11 more apples at k dollars each. The total cost can be represented as 10 k + 17 − 7 j − 18 − 11 k , which simplifies to − 7 j − k − 1 .
The expression 10 k + 17 − 7 j − 18 − 11 k simplifies to − 7 j − k − 1 . This matches Option B from the choices given. Thus, the answer is − 7 j − k − 1 .
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