Rationale
-4x - 3
To simplify the expression (3x - 5) + (-7x + 2), we combine like terms by adding the coefficients of x and the constant terms. This results in -4x for the x terms and -3 for the constant terms.
A) The expression -4x² - 3 suggests a quadratic term, which is produced when multiplying or squaring terms. However, the original expression contains only linear terms and constants, making this option incorrect as there are no squared terms present.
B) The correct simplification, -4x - 3, is achieved by combining the x terms (3x - 7x = -4x) and the constant terms (-5 + 2 = -3). This matches the simplified form required.
C) The number 28 does not relate to the simplification of the given expression. It does not account for any of the terms present in (3x - 5) + (-7x + 2) and is therefore irrelevant to the problem.
D) Like option A, -4x² - 10 incorrectly implies the presence of a quadratic term. The expression only simplifies to linear terms and constants, rendering this option invalid as well.
Conclusion
The simplification of the expression (3x - 5) + (-7x + 2) leads to the correct answer of -4x - 3, achieved by combining like terms. Other options incorrectly introduce quadratic terms or unrelated constants, highlighting the importance of careful term management in algebraic simplification.