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Simplifying 3(5z + -1) + -2(z + 8) = 6(z + 1) Reorder the terms: 3(-1 + 5z) + -2(z + 8) = 6(z + 1) (-1 * 3 + 5z * 3) + -2(z + 8) = 6(z + 1) (-3 + 15z) + -2(z + 8) = 6(z + 1) Reorder the terms: -3 + 15z + -2(8 + z) = 6(z + 1) -3 + 15z + (8 * -2 + z * -2) = 6(z + 1) -3 + 15z + (-16 + -2z) = 6(z + 1) Reorder the terms: -3 + -16 + 15z + -2z = 6(z + 1) Combine like terms: -3 + -16 = -19 -19 + 15z + -2z = 6(z + 1) Combine like terms: 15z + -2z = 13z -19 + 13z = 6(z + 1) Reorder the terms: -19 + 13z = 6(1 + z) -19 + 13z = (1 * 6 + z * 6) -19 + 13z = (6 + 6z) Solving -19 + 13z = 6 + 6z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-6z' to each side of the equation. -19 + 13z + -6z = 6 + 6z + -6z Combine like terms: 13z + -6z = 7z -19 + 7z = 6 + 6z + -6z Combine like terms: 6z + -6z = 0 -19 + 7z = 6 + 0 -19 + 7z = 6 Add '19' to each side of the equation. -19 + 19 + 7z = 6 + 19 Combine like terms: -19 + 19 = 0 0 + 7z = 6 + 19 7z = 6 + 19 Combine like terms: 6 + 19 = 25 7z = 25 Divide each side by '7'. z = 3.571428571 Simplifying z = 3.571428571
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