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