Which expression is equivalent to $4 x-9+6 y+17 x$?
A. $17 x+6 y+4 x-9$
B. $9+6 y-4 x+17 x$
C. $(4 x+17 x)-(9+6 y)$
D. $(4 x+6 y)-(9+17 x)$
Answer (2)
Combine like terms: 4 x + 17 x = 21 x .
Rewrite the expression: 21 x − 9 + 6 y .
Rearrange the terms: 21 x + 6 y − 9 .
The equivalent expression is: 21 x + 6 y − 9 .
Explanation
Understanding the Problem We are given the expression 4 x − 9 + 6 y + 17 x and asked to find an equivalent expression from the given options. To do this, we need to combine like terms in the given expression.
Combining Like Terms First, let's identify the like terms. We have 4 x and 17 x as like terms. Combining these, we get 4 x + 17 x = ( 4 + 17 ) x = 21 x . So the expression becomes 21 x − 9 + 6 y .
Rearranging Terms Now, let's rearrange the terms to match the typical form with the x term first, then the y term, and finally the constant term: 21 x + 6 y − 9 .
Checking the Options Now we check the given options: Option 1: 17 x + 6 y + 4 x − 9 = ( 17 + 4 ) x + 6 y − 9 = 21 x + 6 y − 9 . This is equivalent to our simplified expression. Option 2: 9 + 6 y − 4 x + 17 x = 9 + 6 y + ( 17 − 4 ) x = 9 + 6 y + 13 x . This is not equivalent. Option 3: ( 4 x + 17 x ) − ( 9 + 6 y ) = 21 x − 9 − 6 y = 21 x − 6 y − 9 . This is not equivalent. Option 4: ( 4 x + 6 y ) − ( 9 + 17 x ) = 4 x + 6 y − 9 − 17 x = ( 4 − 17 ) x + 6 y − 9 = − 13 x + 6 y − 9 . This is not equivalent.
Final Answer The expression equivalent to 4 x − 9 + 6 y + 17 x is 21 x + 6 y − 9 , which matches option 1.
Examples
Combining like terms is a fundamental skill in algebra, used in various real-life scenarios. For instance, imagine you're calculating the total cost of items at a store. If you buy 4 apples at $x each and later decide to buy 17 more apples at the same price, the total cost for the apples alone would be 4 x + 17 x . Simplifying this to 21 x helps you quickly determine the total cost without having to calculate each purchase separately. This principle applies to budgeting, inventory management, and many other practical situations where combining similar quantities simplifies calculations.
The expression 4 x − 9 + 6 y + 17 x simplifies to 21 x + 6 y − 9 . After checking the answer choices, the equivalent expression is found in Option A, which is 17 x + 6 y + 4 x − 9 . This choice matches the simplified form of the original expression.
;
