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Simplifying (z + -4z) = 7z + -1(1 + -1z) Combine like terms: z + -4z = -3z (-3z) = 7z + -1(1 + -1z) (-3z) = 7z + -1(1 + -1z) (-3z) = 7z + (1 * -1 + -1z * -1) (-3z) = 7z + (-1 + 1z) Reorder the terms: (-3z) = -1 + 7z + 1z Combine like terms: 7z + 1z = 8z (-3z) = -1 + 8z Solving (-3z) = -1 + 8z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-8z' to each side of the equation. (-3z) + -8z = -1 + 8z + -8z Combine like terms: (-3z) + -8z = -11z -11z = -1 + 8z + -8z Combine like terms: 8z + -8z = 0 -11z = -1 + 0 -11z = -1 Divide each side by '-11'. z = 0.09090909091 Simplifying z = 0.09090909091
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