Justify each step of the following direct proof, which shows that if x is a real number, then x·0 = 0. Assume that the following are previous theorems: If a, b, and care real numbers, then b + 0 = b and a (b+ c) = ab + ac. If a + b = a+ c, then b = c.
Proof x· 0 + 0 = x · 0 = x · (0 + 0) = x · 0 + x · 0; therefore, x · 0 = 0.
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