Simplify: (3x - 5) + (-7x + 2)

Rationale

-4x - 3

To simplify the expression (3x - 5) + (-7x + 2), we first combine like terms, resulting in -4x - 3. This reveals the simplified form of the expression, which correctly represents the total value after combining the terms.

A (-4x² - 3) YOUR ANSWER

This choice suggests a quadratic term (-4x²), which is incorrect as the original expression contains only linear terms. The simplification process does not yield any squared terms, making this option invalid.

B (-4x - 3) CORRECT

This is the correct choice as it accurately represents the sum of the like terms from the expression. By combining 3x and -7x, we get -4x, and combining -5 and +2 results in -3, leading to the final simplified expression of -4x - 3.

C (28) YOUR ANSWER

This choice indicates a constant value that does not relate to the expression provided. The original expression involves variables and their coefficients, thus simplifying it cannot yield a numeric constant like 28.

D (-4x² - 10) YOUR ANSWER

Similar to choice A, this option introduces a quadratic term (-4x²) that does not exist in the original expression. The simplification process only involves linear terms and constant values, making this option also incorrect.

Conclusion

The correct simplification of the expression (3x - 5) + (-7x + 2) results in -4x - 3, which accurately combines the linear terms and constants present. The other options incorrectly introduce non-existent terms or constants, failing to represent the simplified form of the expression. Understanding how to combine like terms is essential for accurate algebraic simplification.

Simplify: (3x - 5) + (-7x + 2)

-4x - 3

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