Use the distributive and commutative properties to determine
whether each pair of expressions is equivalent for all values of x.
a. 3x + 7x and 10x
b. 5x and 5x – 10x c. 4(1 + 2x) - 3x and 5x + 4 d. 5 - 3(2 – 4x) and -1 + 12x

a. equivalent

b. not equivalent

c. equivalent

d. equivalent

Step-by-step explanation:

a. 3x +7x = (3+7)x = 10x . . . equivalent to 10x

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b. 5x -10x = (5 -10)x = -5x . . . not equivalent to 5x

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c. 4(1 +2x) -3x = 4·1 +4·2x -3x = 4 +(8 -3)x = 4 +5x = 5x +4 . . . equivalent to 5x +4

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d. 5 -3(2 -4x) = 5 -3·2 -3(-4x) = 5 -6 +12x = -1 +12x . . . equivalent to -1 +12x

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