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Simplifying 3z + 2(6 + -1z) = -1(z + -1) + 5 3z + (6 * 2 + -1z * 2) = -1(z + -1) + 5 3z + (12 + -2z) = -1(z + -1) + 5 Reorder the terms: 12 + 3z + -2z = -1(z + -1) + 5 Combine like terms: 3z + -2z = 1z 12 + 1z = -1(z + -1) + 5 Reorder the terms: 12 + 1z = -1(-1 + z) + 5 12 + 1z = (-1 * -1 + z * -1) + 5 12 + 1z = (1 + -1z) + 5 Reorder the terms: 12 + 1z = 1 + 5 + -1z Combine like terms: 1 + 5 = 6 12 + 1z = 6 + -1z Solving 12 + 1z = 6 + -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 = 6 + -1z + z Combine like terms: 1z + z = 2z 12 + 2z = 6 + -1z + z Combine like terms: -1z + z = 0 12 + 2z = 6 + 0 12 + 2z = 6 Add '-12' to each side of the equation. 12 + -12 + 2z = 6 + -12 Combine like terms: 12 + -12 = 0 0 + 2z = 6 + -12 2z = 6 + -12 Combine like terms: 6 + -12 = -6 2z = -6 Divide each side by '2'. z = -3 Simplifying z = -3
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