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a. By the distributive property, 3x + 7x = (3+7)x = 10x, so this is always true.

b. By the distributive property, 5x-10x = (5-10)x = -5x, which is not necessarily equal to 5x (if you let x equal any value other than zero, you will see that this does not hold).

c. 4(1 + 2x) - 3x is equal to (4 + 8x) - 3x (by the distributive property), which is equal to 4 + 5x. This is equal to 5x + 4 since addition is commutative.

d. 5 - 3(2 - 4x) = 5 - (6 - 12x) = -1 + 12x, so this does hold for all values of x.

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