Final answer:
To simplify the expression ((-5x-3y)-(-x-3z)), we distribute the negative sign, combine like terms, and simplify, resulting in -4x-3y+3z. The options given do not directly correspond to these steps, suggesting a potential issue with the question.
Step-by-step explanation:
The student is asking which facts could simplify the expression ((-5x-3y)-(-x-3z)). To simplify this expression, we need to apply the distributive property and the rules for adding and subtracting signed numbers.
- First, distribute the negative sign inside the second parenthesis: ((-5x-3y)+x+3z).
- Then, combine like terms: (-5x+x)+(-3y)+(3z).
- Finally, simplify the expression: -4x-3y+3z.
Therefore, the facts that could be applied to simplify this expression are:
- B. (-3y+3z) - This represents the combination of -3y and +3z.
- D. (-2x+3y-3z) - We don't use 2x, but the signs for y and z are correct. After adjusting for the correct coefficient of x (-4x), option D is partially correct.
- Since no perfect match options are given for -4x and no option contains just -4x as a fact, we can only conclude that the list provided may be incomplete or does not perfectly correspond to the expression that needs simplifying.
Note that the provided options do not directly translate to the simplified form of the original expression, which is -4x-3y+3z. Hence, none of the options given (A, B, C, D), when taken literally and applied, would result in the correct simplified form of the original expression. This could be a typo or mistake in the options list.