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Simplifying 5(3z + -1) + -5(2 + 6) = 6(z + 1) Reorder the terms: 5(-1 + 3z) + -5(2 + 6) = 6(z + 1) (-1 * 5 + 3z * 5) + -5(2 + 6) = 6(z + 1) (-5 + 15z) + -5(2 + 6) = 6(z + 1) Combine like terms: 2 + 6 = 8 -5 + 15z + -5(8) = 6(z + 1) Multiply -5 * 8 -5 + 15z + -40 = 6(z + 1) Reorder the terms: -5 + -40 + 15z = 6(z + 1) Combine like terms: -5 + -40 = -45 -45 + 15z = 6(z + 1) Reorder the terms: -45 + 15z = 6(1 + z) -45 + 15z = (1 * 6 + z * 6) -45 + 15z = (6 + 6z) Solving -45 + 15z = 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. -45 + 15z + -6z = 6 + 6z + -6z Combine like terms: 15z + -6z = 9z -45 + 9z = 6 + 6z + -6z Combine like terms: 6z + -6z = 0 -45 + 9z = 6 + 0 -45 + 9z = 6 Add '45' to each side of the equation. -45 + 45 + 9z = 6 + 45 Combine like terms: -45 + 45 = 0 0 + 9z = 6 + 45 9z = 6 + 45 Combine like terms: 6 + 45 = 51 9z = 51 Divide each side by '9'. z = 5.666666667 Simplifying z = 5.666666667
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