Which of the following expressions is equivalent to $2 x+y-4 y+8$?
A. $2 x-4 y+8$
B. $2 x+3 y+8$
C. $3 x-4 y+8$
D. $2 x-3 y+8$
Answer (1)
Combine the 'y' terms: y − 4 y = − 3 y .
Substitute the combined term back into the original expression: 2 x + y − 4 y + 8 = 2 x − 3 y + 8 .
The equivalent expression is 2 x − 3 y + 8 .
Explanation
Understanding the Problem We are given the expression 2 x + y − 4 y + 8 and asked to find an equivalent expression from the given options. To do this, we need to combine the like terms in the expression.
Combining Like Terms The expression contains two terms involving y , namely y and − 4 y . Combining these terms, we have y − 4 y = ( 1 − 4 ) y . From the tool, we know that 1 − 4 = − 3 . Therefore, y − 4 y = − 3 y .
Simplifying the Expression Substituting this back into the original expression, we get 2 x + y − 4 y + 8 = 2 x − 3 y + 8 .
Finding the Equivalent Expression Comparing this simplified expression with the given options, we see that the equivalent expression is 2 x − 3 y + 8 .
Final Answer Therefore, the expression equivalent to 2 x + y − 4 y + 8 is 2 x − 3 y + 8 .
Examples
In retail, simplifying expressions can help manage inventory. For example, if a store has 2 x items of one product, adds y items, removes 4 y items due to returns, and then receives 8 more items, the expression 2 x + y − 4 y + 8 represents the final inventory. Simplifying this to 2 x − 3 y + 8 allows for quick assessment of stock levels and efficient restocking decisions.
