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