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Simplifying -3(4z + -1) + -2(z + -1) = 8(z + 1) Reorder the terms: -3(-1 + 4z) + -2(z + -1) = 8(z + 1) (-1 * -3 + 4z * -3) + -2(z + -1) = 8(z + 1) (3 + -12z) + -2(z + -1) = 8(z + 1) Reorder the terms: 3 + -12z + -2(-1 + z) = 8(z + 1) 3 + -12z + (-1 * -2 + z * -2) = 8(z + 1) 3 + -12z + (2 + -2z) = 8(z + 1) Reorder the terms: 3 + 2 + -12z + -2z = 8(z + 1) Combine like terms: 3 + 2 = 5 5 + -12z + -2z = 8(z + 1) Combine like terms: -12z + -2z = -14z 5 + -14z = 8(z + 1) Reorder the terms: 5 + -14z = 8(1 + z) 5 + -14z = (1 * 8 + z * 8) 5 + -14z = (8 + 8z) Solving 5 + -14z = 8 + 8z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-8z' to each side of the equation. 5 + -14z + -8z = 8 + 8z + -8z Combine like terms: -14z + -8z = -22z 5 + -22z = 8 + 8z + -8z Combine like terms: 8z + -8z = 0 5 + -22z = 8 + 0 5 + -22z = 8 Add '-5' to each side of the equation. 5 + -5 + -22z = 8 + -5 Combine like terms: 5 + -5 = 0 0 + -22z = 8 + -5 -22z = 8 + -5 Combine like terms: 8 + -5 = 3 -22z = 3 Divide each side by '-22'. z = -0.1363636364 Simplifying z = -0.1363636364
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