Question

show that if y=?(1-x)z, then 1-y=(1-x)(1-z) +x

Answer 1

Answer on Question #44572 - Math - Algebra

Show that if $y = ?(1-x)z$, then $1-y = (1-x)(1-z) + x$.

Solution.

If $y = (1 - x)z \Rightarrow -y = -(1 - x)z \Rightarrow 1 - y = -(1 - x)z + 1 = -(1 - x)(z - 1 + 1) + 1 = - (1 - x)(z - 1) - (1 - x) + 1 = -(1 - x)(z - 1) - 1 + x + 1 = (1 - x)(1 - z) + x$.

Answer: if $y = (1 - x)z$, then $1 - y = (1 - x)(1 - z) + x$.

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