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Simplifying -1[8z + -1(12z + 5)] = 5 + (3z + 1) Reorder the terms: -1[8z + -1(5 + 12z)] = 5 + (3z + 1) -1[8z + (5 * -1 + 12z * -1)] = 5 + (3z + 1) -1[8z + (-5 + -12z)] = 5 + (3z + 1) Reorder the terms: -1[-5 + 8z + -12z] = 5 + (3z + 1) Combine like terms: 8z + -12z = -4z -1[-5 + -4z] = 5 + (3z + 1) [-5 * -1 + -4z * -1] = 5 + (3z + 1) [5 + 4z] = 5 + (3z + 1) Reorder the terms: 5 + 4z = 5 + (1 + 3z) Remove parenthesis around (1 + 3z) 5 + 4z = 5 + 1 + 3z Combine like terms: 5 + 1 = 6 5 + 4z = 6 + 3z Solving 5 + 4z = 6 + 3z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-3z' to each side of the equation. 5 + 4z + -3z = 6 + 3z + -3z Combine like terms: 4z + -3z = 1z 5 + 1z = 6 + 3z + -3z Combine like terms: 3z + -3z = 0 5 + 1z = 6 + 0 5 + 1z = 6 Add '-5' to each side of the equation. 5 + -5 + 1z = 6 + -5 Combine like terms: 5 + -5 = 0 0 + 1z = 6 + -5 1z = 6 + -5 Combine like terms: 6 + -5 = 1 1z = 1 Divide each side by '1'. z = 1 Simplifying z = 1
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