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Simplifying 3z + 2(6 + -1z) = -1(z + -2) + 8 3z + (6 * 2 + -1z * 2) = -1(z + -2) + 8 3z + (12 + -2z) = -1(z + -2) + 8 Reorder the terms: 12 + 3z + -2z = -1(z + -2) + 8 Combine like terms: 3z + -2z = 1z 12 + 1z = -1(z + -2) + 8 Reorder the terms: 12 + 1z = -1(-2 + z) + 8 12 + 1z = (-2 * -1 + z * -1) + 8 12 + 1z = (2 + -1z) + 8 Reorder the terms: 12 + 1z = 2 + 8 + -1z Combine like terms: 2 + 8 = 10 12 + 1z = 10 + -1z Solving 12 + 1z = 10 + -1z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add 'z' to each side of the equation. 12 + 1z + z = 10 + -1z + z Combine like terms: 1z + z = 2z 12 + 2z = 10 + -1z + z Combine like terms: -1z + z = 0 12 + 2z = 10 + 0 12 + 2z = 10 Add '-12' to each side of the equation. 12 + -12 + 2z = 10 + -12 Combine like terms: 12 + -12 = 0 0 + 2z = 10 + -12 2z = 10 + -12 Combine like terms: 10 + -12 = -2 2z = -2 Divide each side by '2'. z = -1 Simplifying z = -1
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