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Simplifying 5(3z + -1) + -5(z + 6) = 8(z + 1) Reorder the terms: 5(-1 + 3z) + -5(z + 6) = 8(z + 1) (-1 * 5 + 3z * 5) + -5(z + 6) = 8(z + 1) (-5 + 15z) + -5(z + 6) = 8(z + 1) Reorder the terms: -5 + 15z + -5(6 + z) = 8(z + 1) -5 + 15z + (6 * -5 + z * -5) = 8(z + 1) -5 + 15z + (-30 + -5z) = 8(z + 1) Reorder the terms: -5 + -30 + 15z + -5z = 8(z + 1) Combine like terms: -5 + -30 = -35 -35 + 15z + -5z = 8(z + 1) Combine like terms: 15z + -5z = 10z -35 + 10z = 8(z + 1) Reorder the terms: -35 + 10z = 8(1 + z) -35 + 10z = (1 * 8 + z * 8) -35 + 10z = (8 + 8z) Solving -35 + 10z = 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. -35 + 10z + -8z = 8 + 8z + -8z Combine like terms: 10z + -8z = 2z -35 + 2z = 8 + 8z + -8z Combine like terms: 8z + -8z = 0 -35 + 2z = 8 + 0 -35 + 2z = 8 Add '35' to each side of the equation. -35 + 35 + 2z = 8 + 35 Combine like terms: -35 + 35 = 0 0 + 2z = 8 + 35 2z = 8 + 35 Combine like terms: 8 + 35 = 43 2z = 43 Divide each side by '2'. z = 21.5 Simplifying z = 21.5
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