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Simplifying 3z + 2(4 + -1z) = -1(z + -4) + 2 3z + (4 * 2 + -1z * 2) = -1(z + -4) + 2 3z + (8 + -2z) = -1(z + -4) + 2 Reorder the terms: 8 + 3z + -2z = -1(z + -4) + 2 Combine like terms: 3z + -2z = 1z 8 + 1z = -1(z + -4) + 2 Reorder the terms: 8 + 1z = -1(-4 + z) + 2 8 + 1z = (-4 * -1 + z * -1) + 2 8 + 1z = (4 + -1z) + 2 Reorder the terms: 8 + 1z = 4 + 2 + -1z Combine like terms: 4 + 2 = 6 8 + 1z = 6 + -1z Solving 8 + 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. 8 + 1z + z = 6 + -1z + z Combine like terms: 1z + z = 2z 8 + 2z = 6 + -1z + z Combine like terms: -1z + z = 0 8 + 2z = 6 + 0 8 + 2z = 6 Add '-8' to each side of the equation. 8 + -8 + 2z = 6 + -8 Combine like terms: 8 + -8 = 0 0 + 2z = 6 + -8 2z = 6 + -8 Combine like terms: 6 + -8 = -2 2z = -2 Divide each side by '2'. z = -1 Simplifying z = -1
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