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Simplifying -1[7z + -1(13z + 1)] = 1 + (5z + 5) Reorder the terms: -1[7z + -1(1 + 13z)] = 1 + (5z + 5) -1[7z + (1 * -1 + 13z * -1)] = 1 + (5z + 5) -1[7z + (-1 + -13z)] = 1 + (5z + 5) Reorder the terms: -1[-1 + 7z + -13z] = 1 + (5z + 5) Combine like terms: 7z + -13z = -6z -1[-1 + -6z] = 1 + (5z + 5) [-1 * -1 + -6z * -1] = 1 + (5z + 5) [1 + 6z] = 1 + (5z + 5) Reorder the terms: 1 + 6z = 1 + (5 + 5z) Remove parenthesis around (5 + 5z) 1 + 6z = 1 + 5 + 5z Combine like terms: 1 + 5 = 6 1 + 6z = 6 + 5z Solving 1 + 6z = 6 + 5z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-5z' to each side of the equation. 1 + 6z + -5z = 6 + 5z + -5z Combine like terms: 6z + -5z = 1z 1 + 1z = 6 + 5z + -5z Combine like terms: 5z + -5z = 0 1 + 1z = 6 + 0 1 + 1z = 6 Add '-1' to each side of the equation. 1 + -1 + 1z = 6 + -1 Combine like terms: 1 + -1 = 0 0 + 1z = 6 + -1 1z = 6 + -1 Combine like terms: 6 + -1 = 5 1z = 5 Divide each side by '1'. z = 5 Simplifying z = 5
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