Question

Simplify the algebraic expression below 2(x+y+7)-3(x+2y-2)+2(x-y-5)

A. -x + 25
B. -x - 5
C. x + 25
D. x - 5

Answer 1

After distributing and combining like terms, the algebraic expression simplifies to x + 10, which does not match any of the provided options.

Step-by-step explanation:

To simplify the algebraic expression 2(x+y+7)-3(x+2y-2)+2(x-y-5), let's distribute the coefficients and combine like terms.

• Distribute the 2 to each term in the first parentheses: 2x + 2y + 14.
• Distribute the -3 to each term in the second parentheses: -3x - 6y + 6.
• Distribute the 2 to each term in the third parentheses: 2x - 2y - 10.

Now combine like terms:

• x-terms: 2x - 3x + 2x = 1x or x.
• y-terms: 2y - 6y - 2y = -6y.
• Constant terms: 14 + 6 - 10 = 10.

Since there are no y terms to combine with, the simplified expression is x + 10. Therefore, the answer as it is not listed among the options provided is that the given alternatives are incorrect.