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Simplifying -1[4z + -1(12z + 2)] = 2 + -1(7z + 8) Reorder the terms: -1[4z + -1(2 + 12z)] = 2 + -1(7z + 8) -1[4z + (2 * -1 + 12z * -1)] = 2 + -1(7z + 8) -1[4z + (-2 + -12z)] = 2 + -1(7z + 8) Reorder the terms: -1[-2 + 4z + -12z] = 2 + -1(7z + 8) Combine like terms: 4z + -12z = -8z -1[-2 + -8z] = 2 + -1(7z + 8) [-2 * -1 + -8z * -1] = 2 + -1(7z + 8) [2 + 8z] = 2 + -1(7z + 8) Reorder the terms: 2 + 8z = 2 + -1(8 + 7z) 2 + 8z = 2 + (8 * -1 + 7z * -1) 2 + 8z = 2 + (-8 + -7z) Combine like terms: 2 + -8 = -6 2 + 8z = -6 + -7z Solving 2 + 8z = -6 + -7z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '7z' to each side of the equation. 2 + 8z + 7z = -6 + -7z + 7z Combine like terms: 8z + 7z = 15z 2 + 15z = -6 + -7z + 7z Combine like terms: -7z + 7z = 0 2 + 15z = -6 + 0 2 + 15z = -6 Add '-2' to each side of the equation. 2 + -2 + 15z = -6 + -2 Combine like terms: 2 + -2 = 0 0 + 15z = -6 + -2 15z = -6 + -2 Combine like terms: -6 + -2 = -8 15z = -8 Divide each side by '15'. z = -0.5333333333 Simplifying z = -0.5333333333
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