Which best proves why the expressions 4 times open paren x plus 3 close paren plus 2 x and 6 times open paren x plus 2 close paren must be equivalent expressions?

Distribute and combine like terms: 4(x + 3) + 2x = 4x + 12 + 2x = 6x + 12, and 6(x + 2) = 6x + 12. The expressions are therefore equivalent for every value of x. Choice C also gives matching values at x = 1 and x = 8; checking examples supports the result, though the algebraic simplification is what proves it must hold.

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