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Simplify: (−9a − 20c) − (−15a + 3c) − (−22a − 7c)

A. −2a − 24c
B. −16a − 16c
C. 28a − 16c
D. 28a − 24c

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Final answer:

The simplified form of the expression (−9a − 20c) − (−15a + 3c) − (−22a − 7c) is 28a − 16c, which is option C.

Step-by-step explanation:

Simplifying the ExpressionTo simplify the expression (−9a − 20c) − (−15a + 3c) − (−22a − 7c), we need to perform subtraction by adding the opposites. First, distribute the negative sign in the second and third parentheses to every term inside:To simplify the expression (−9a − 20c) − (−15a + 3c) − (−22a − 7c), we can remove the parentheses and perform the subtraction.

This results in -9a - 20c + 15a - 3c + 22a + 7c. Next, we can combine like terms by adding or subtracting the coefficients of the same variables. This gives us (-9a + 15a + 22a) + (-20c - 3c + 7c), which simplifies to 28a - 16c.−9a − 20c + 15a − 3c + 22a + 7cNext, combine like terms (terms with the same variables):(−9a + 15a + 22a) + (−20c − 3c + 7c)Solve for each group of like terms:(28a) + (−16cSo the simplified form of the expression is:28a − 16cThis corresponds to option C.

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