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Simplifying -1[3z + -1(5z + 1)] = 1 + (1z + 6) Reorder the terms: -1[3z + -1(1 + 5z)] = 1 + (1z + 6) -1[3z + (1 * -1 + 5z * -1)] = 1 + (1z + 6) -1[3z + (-1 + -5z)] = 1 + (1z + 6) Reorder the terms: -1[-1 + 3z + -5z] = 1 + (1z + 6) Combine like terms: 3z + -5z = -2z -1[-1 + -2z] = 1 + (1z + 6) [-1 * -1 + -2z * -1] = 1 + (1z + 6) [1 + 2z] = 1 + (1z + 6) Reorder the terms: 1 + 2z = 1 + (6 + 1z) Remove parenthesis around (6 + 1z) 1 + 2z = 1 + 6 + 1z Combine like terms: 1 + 6 = 7 1 + 2z = 7 + 1z Solving 1 + 2z = 7 + 1z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-1z' to each side of the equation. 1 + 2z + -1z = 7 + 1z + -1z Combine like terms: 2z + -1z = 1z 1 + 1z = 7 + 1z + -1z Combine like terms: 1z + -1z = 0 1 + 1z = 7 + 0 1 + 1z = 7 Add '-1' to each side of the equation. 1 + -1 + 1z = 7 + -1 Combine like terms: 1 + -1 = 0 0 + 1z = 7 + -1 1z = 7 + -1 Combine like terms: 7 + -1 = 6 1z = 6 Divide each side by '1'. z = 6 Simplifying z = 6
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