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Simplifying 5(3z + -1) + -3(z + 5) = 9(z + 1) Reorder the terms: 5(-1 + 3z) + -3(z + 5) = 9(z + 1) (-1 * 5 + 3z * 5) + -3(z + 5) = 9(z + 1) (-5 + 15z) + -3(z + 5) = 9(z + 1) Reorder the terms: -5 + 15z + -3(5 + z) = 9(z + 1) -5 + 15z + (5 * -3 + z * -3) = 9(z + 1) -5 + 15z + (-15 + -3z) = 9(z + 1) Reorder the terms: -5 + -15 + 15z + -3z = 9(z + 1) Combine like terms: -5 + -15 = -20 -20 + 15z + -3z = 9(z + 1) Combine like terms: 15z + -3z = 12z -20 + 12z = 9(z + 1) Reorder the terms: -20 + 12z = 9(1 + z) -20 + 12z = (1 * 9 + z * 9) -20 + 12z = (9 + 9z) Solving -20 + 12z = 9 + 9z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-9z' to each side of the equation. -20 + 12z + -9z = 9 + 9z + -9z Combine like terms: 12z + -9z = 3z -20 + 3z = 9 + 9z + -9z Combine like terms: 9z + -9z = 0 -20 + 3z = 9 + 0 -20 + 3z = 9 Add '20' to each side of the equation. -20 + 20 + 3z = 9 + 20 Combine like terms: -20 + 20 = 0 0 + 3z = 9 + 20 3z = 9 + 20 Combine like terms: 9 + 20 = 29 3z = 29 Divide each side by '3'. z = 9.666666667 Simplifying z = 9.666666667
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