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Simplifying 2(4z + -1) + -2(z + 9) = 8(z + 1) Reorder the terms: 2(-1 + 4z) + -2(z + 9) = 8(z + 1) (-1 * 2 + 4z * 2) + -2(z + 9) = 8(z + 1) (-2 + 8z) + -2(z + 9) = 8(z + 1) Reorder the terms: -2 + 8z + -2(9 + z) = 8(z + 1) -2 + 8z + (9 * -2 + z * -2) = 8(z + 1) -2 + 8z + (-18 + -2z) = 8(z + 1) Reorder the terms: -2 + -18 + 8z + -2z = 8(z + 1) Combine like terms: -2 + -18 = -20 -20 + 8z + -2z = 8(z + 1) Combine like terms: 8z + -2z = 6z -20 + 6z = 8(z + 1) Reorder the terms: -20 + 6z = 8(1 + z) -20 + 6z = (1 * 8 + z * 8) -20 + 6z = (8 + 8z) Solving -20 + 6z = 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. -20 + 6z + -8z = 8 + 8z + -8z Combine like terms: 6z + -8z = -2z -20 + -2z = 8 + 8z + -8z Combine like terms: 8z + -8z = 0 -20 + -2z = 8 + 0 -20 + -2z = 8 Add '20' to each side of the equation. -20 + 20 + -2z = 8 + 20 Combine like terms: -20 + 20 = 0 0 + -2z = 8 + 20 -2z = 8 + 20 Combine like terms: 8 + 20 = 28 -2z = 28 Divide each side by '-2'. z = -14 Simplifying z = -14
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