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Simplifying 5(4z + -1) + -5(z + 3) = 6(z + 1) Reorder the terms: 5(-1 + 4z) + -5(z + 3) = 6(z + 1) (-1 * 5 + 4z * 5) + -5(z + 3) = 6(z + 1) (-5 + 20z) + -5(z + 3) = 6(z + 1) Reorder the terms: -5 + 20z + -5(3 + z) = 6(z + 1) -5 + 20z + (3 * -5 + z * -5) = 6(z + 1) -5 + 20z + (-15 + -5z) = 6(z + 1) Reorder the terms: -5 + -15 + 20z + -5z = 6(z + 1) Combine like terms: -5 + -15 = -20 -20 + 20z + -5z = 6(z + 1) Combine like terms: 20z + -5z = 15z -20 + 15z = 6(z + 1) Reorder the terms: -20 + 15z = 6(1 + z) -20 + 15z = (1 * 6 + z * 6) -20 + 15z = (6 + 6z) Solving -20 + 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. -20 + 15z + -6z = 6 + 6z + -6z Combine like terms: 15z + -6z = 9z -20 + 9z = 6 + 6z + -6z Combine like terms: 6z + -6z = 0 -20 + 9z = 6 + 0 -20 + 9z = 6 Add '20' to each side of the equation. -20 + 20 + 9z = 6 + 20 Combine like terms: -20 + 20 = 0 0 + 9z = 6 + 20 9z = 6 + 20 Combine like terms: 6 + 20 = 26 9z = 26 Divide each side by '9'. z = 2.888888889 Simplifying z = 2.888888889
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