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Simplifying -1(z + 6) + (32 + 1) = -3(z + 1) Reorder the terms: -1(6 + z) + (32 + 1) = -3(z + 1) (6 * -1 + z * -1) + (32 + 1) = -3(z + 1) (-6 + -1z) + (32 + 1) = -3(z + 1) Combine like terms: 32 + 1 = 33 -6 + -1z + (33) = -3(z + 1) -6 + -1z + 33 = -3(z + 1) Reorder the terms: -6 + 33 + -1z = -3(z + 1) Combine like terms: -6 + 33 = 27 27 + -1z = -3(z + 1) Reorder the terms: 27 + -1z = -3(1 + z) 27 + -1z = (1 * -3 + z * -3) 27 + -1z = (-3 + -3z) Solving 27 + -1z = -3 + -3z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '3z' to each side of the equation. 27 + -1z + 3z = -3 + -3z + 3z Combine like terms: -1z + 3z = 2z 27 + 2z = -3 + -3z + 3z Combine like terms: -3z + 3z = 0 27 + 2z = -3 + 0 27 + 2z = -3 Add '-27' to each side of the equation. 27 + -27 + 2z = -3 + -27 Combine like terms: 27 + -27 = 0 0 + 2z = -3 + -27 2z = -3 + -27 Combine like terms: -3 + -27 = -30 2z = -30 Divide each side by '2'. z = -15 Simplifying z = -15
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