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Answer:

(p - 5 + 3a) - (6p - 4a + 1):          original expression

(p - 5 + 3a) + (- (6p - 4a + 1)):     subtraction as adding the opposite

(p - 5 + 3a) + (-6p) + 4a + (-1):    the opposite of a sum is the sum of the opposites

p + (-6p) + 3a + 4a + (-5) + (-1):    any order, any grouping

(-5p) + 7a + (-6):                          combine like terms

-5p + 7a - 6:                                adding the inverse is subtracting

Step-by-step explanation:

(p - 5 + 3a) - (6p - 4a + 1):          original expression

(p - 5 + 3a) + (- (6p - 4a + 1)):     subtraction as adding the opposite

(p - 5 + 3a) + (-6p) + 4a + (-1):    the opposite of a sum is the sum of the opposites

p + (-6p) + 3a + 4a + (-5) + (-1):    any order, any grouping

(-5p) + 7a + (-6):                          combine like terms

-5p + 7a - 6:                                adding the inverse is subtracting

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