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Simplifying 5(3z + -1) + -2(z + 7) = 8(z + 1) Reorder the terms: 5(-1 + 3z) + -2(z + 7) = 8(z + 1) (-1 * 5 + 3z * 5) + -2(z + 7) = 8(z + 1) (-5 + 15z) + -2(z + 7) = 8(z + 1) Reorder the terms: -5 + 15z + -2(7 + z) = 8(z + 1) -5 + 15z + (7 * -2 + z * -2) = 8(z + 1) -5 + 15z + (-14 + -2z) = 8(z + 1) Reorder the terms: -5 + -14 + 15z + -2z = 8(z + 1) Combine like terms: -5 + -14 = -19 -19 + 15z + -2z = 8(z + 1) Combine like terms: 15z + -2z = 13z -19 + 13z = 8(z + 1) Reorder the terms: -19 + 13z = 8(1 + z) -19 + 13z = (1 * 8 + z * 8) -19 + 13z = (8 + 8z) Solving -19 + 13z = 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. -19 + 13z + -8z = 8 + 8z + -8z Combine like terms: 13z + -8z = 5z -19 + 5z = 8 + 8z + -8z Combine like terms: 8z + -8z = 0 -19 + 5z = 8 + 0 -19 + 5z = 8 Add '19' to each side of the equation. -19 + 19 + 5z = 8 + 19 Combine like terms: -19 + 19 = 0 0 + 5z = 8 + 19 5z = 8 + 19 Combine like terms: 8 + 19 = 27 5z = 27 Divide each side by '5'. z = 5.4 Simplifying z = 5.4
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