(2x + 3y - 7) - (2x - 3y - 8) Which of the following is equivalent to the preceding expression?

Rationale

6y + 1 is equivalent to the expression (2x + 3y - 7) - (2x - 3y - 8).

To simplify the expression, we first distribute the negative sign across the second set of parentheses, which leads to (2x + 3y - 7) - 2x + 3y + 8. Combining like terms results in 6y + 1.

A (1) YOUR ANSWER

This choice only represents the constant term in the simplified expression and ignores the variable component. While the final expression includes the number 1, it is not complete without the variable term 6y, making this option incorrect.

B (-15) YOUR ANSWER

This option does not relate to the simplified expression at all. The expression (2x + 3y - 7) - (2x - 3y - 8) results in 6y + 1, and -15 does not appear in any part of that simplification. Thus, this choice is incorrect.

C (6y + 1) CORRECT

This option correctly represents the simplified form of the original expression. After distributing the negative sign and combining like terms, we end up with 6y + 1, which is the exact answer we are looking for.

D (6y-15) YOUR ANSWER

This choice has the correct variable term, but the constant is incorrect. The simplified expression yields a constant of 1, not -15. Therefore, while it shares the variable part, the overall expression does not match.

Conclusion

The process of simplifying the expression (2x + 3y - 7) - (2x - 3y - 8) clearly shows that the correct equivalent expression is 6y + 1. The other options either misrepresent the variables or the constants, highlighting the importance of careful simplification in algebraic expressions.

(2x + 3y - 7) - (2x - 3y - 8) Which of the following is equivalent to the preceding expression?

6y + 1 is equivalent to the expression (2x + 3y - 7) - (2x - 3y - 8).

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