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Simplifying 3(5z + -1) + -5(z + 4) = 8(z + 1) Reorder the terms: 3(-1 + 5z) + -5(z + 4) = 8(z + 1) (-1 * 3 + 5z * 3) + -5(z + 4) = 8(z + 1) (-3 + 15z) + -5(z + 4) = 8(z + 1) Reorder the terms: -3 + 15z + -5(4 + z) = 8(z + 1) -3 + 15z + (4 * -5 + z * -5) = 8(z + 1) -3 + 15z + (-20 + -5z) = 8(z + 1) Reorder the terms: -3 + -20 + 15z + -5z = 8(z + 1) Combine like terms: -3 + -20 = -23 -23 + 15z + -5z = 8(z + 1) Combine like terms: 15z + -5z = 10z -23 + 10z = 8(z + 1) Reorder the terms: -23 + 10z = 8(1 + z) -23 + 10z = (1 * 8 + z * 8) -23 + 10z = (8 + 8z) Solving -23 + 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. -23 + 10z + -8z = 8 + 8z + -8z Combine like terms: 10z + -8z = 2z -23 + 2z = 8 + 8z + -8z Combine like terms: 8z + -8z = 0 -23 + 2z = 8 + 0 -23 + 2z = 8 Add '23' to each side of the equation. -23 + 23 + 2z = 8 + 23 Combine like terms: -23 + 23 = 0 0 + 2z = 8 + 23 2z = 8 + 23 Combine like terms: 8 + 23 = 31 2z = 31 Divide each side by '2'. z = 15.5 Simplifying z = 15.5
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