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Simplifying -1[4z + -1(9z + 1)] = 1 + (4z + 8) Reorder the terms: -1[4z + -1(1 + 9z)] = 1 + (4z + 8) -1[4z + (1 * -1 + 9z * -1)] = 1 + (4z + 8) -1[4z + (-1 + -9z)] = 1 + (4z + 8) Reorder the terms: -1[-1 + 4z + -9z] = 1 + (4z + 8) Combine like terms: 4z + -9z = -5z -1[-1 + -5z] = 1 + (4z + 8) [-1 * -1 + -5z * -1] = 1 + (4z + 8) [1 + 5z] = 1 + (4z + 8) Reorder the terms: 1 + 5z = 1 + (8 + 4z) Remove parenthesis around (8 + 4z) 1 + 5z = 1 + 8 + 4z Combine like terms: 1 + 8 = 9 1 + 5z = 9 + 4z Solving 1 + 5z = 9 + 4z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4z' to each side of the equation. 1 + 5z + -4z = 9 + 4z + -4z Combine like terms: 5z + -4z = 1z 1 + 1z = 9 + 4z + -4z Combine like terms: 4z + -4z = 0 1 + 1z = 9 + 0 1 + 1z = 9 Add '-1' to each side of the equation. 1 + -1 + 1z = 9 + -1 Combine like terms: 1 + -1 = 0 0 + 1z = 9 + -1 1z = 9 + -1 Combine like terms: 9 + -1 = 8 1z = 8 Divide each side by '1'. z = 8 Simplifying z = 8
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