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Simplifying -1[7z + -1(12z + 5)] = 5 + (4z + 7) Reorder the terms: -1[7z + -1(5 + 12z)] = 5 + (4z + 7) -1[7z + (5 * -1 + 12z * -1)] = 5 + (4z + 7) -1[7z + (-5 + -12z)] = 5 + (4z + 7) Reorder the terms: -1[-5 + 7z + -12z] = 5 + (4z + 7) Combine like terms: 7z + -12z = -5z -1[-5 + -5z] = 5 + (4z + 7) [-5 * -1 + -5z * -1] = 5 + (4z + 7) [5 + 5z] = 5 + (4z + 7) Reorder the terms: 5 + 5z = 5 + (7 + 4z) Remove parenthesis around (7 + 4z) 5 + 5z = 5 + 7 + 4z Combine like terms: 5 + 7 = 12 5 + 5z = 12 + 4z Solving 5 + 5z = 12 + 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. 5 + 5z + -4z = 12 + 4z + -4z Combine like terms: 5z + -4z = 1z 5 + 1z = 12 + 4z + -4z Combine like terms: 4z + -4z = 0 5 + 1z = 12 + 0 5 + 1z = 12 Add '-5' to each side of the equation. 5 + -5 + 1z = 12 + -5 Combine like terms: 5 + -5 = 0 0 + 1z = 12 + -5 1z = 12 + -5 Combine like terms: 12 + -5 = 7 1z = 7 Divide each side by '1'. z = 7 Simplifying z = 7
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