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Simplifying 3(5z + -1) + -3(z + 2) = 8(z + 1) Reorder the terms: 3(-1 + 5z) + -3(z + 2) = 8(z + 1) (-1 * 3 + 5z * 3) + -3(z + 2) = 8(z + 1) (-3 + 15z) + -3(z + 2) = 8(z + 1) Reorder the terms: -3 + 15z + -3(2 + z) = 8(z + 1) -3 + 15z + (2 * -3 + z * -3) = 8(z + 1) -3 + 15z + (-6 + -3z) = 8(z + 1) Reorder the terms: -3 + -6 + 15z + -3z = 8(z + 1) Combine like terms: -3 + -6 = -9 -9 + 15z + -3z = 8(z + 1) Combine like terms: 15z + -3z = 12z -9 + 12z = 8(z + 1) Reorder the terms: -9 + 12z = 8(1 + z) -9 + 12z = (1 * 8 + z * 8) -9 + 12z = (8 + 8z) Solving -9 + 12z = 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. -9 + 12z + -8z = 8 + 8z + -8z Combine like terms: 12z + -8z = 4z -9 + 4z = 8 + 8z + -8z Combine like terms: 8z + -8z = 0 -9 + 4z = 8 + 0 -9 + 4z = 8 Add '9' to each side of the equation. -9 + 9 + 4z = 8 + 9 Combine like terms: -9 + 9 = 0 0 + 4z = 8 + 9 4z = 8 + 9 Combine like terms: 8 + 9 = 17 4z = 17 Divide each side by '4'. z = 4.25 Simplifying z = 4.25
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