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Simplifying 5(6z + -1) + -2(z + 5) = 13(z + 1) Reorder the terms: 5(-1 + 6z) + -2(z + 5) = 13(z + 1) (-1 * 5 + 6z * 5) + -2(z + 5) = 13(z + 1) (-5 + 30z) + -2(z + 5) = 13(z + 1) Reorder the terms: -5 + 30z + -2(5 + z) = 13(z + 1) -5 + 30z + (5 * -2 + z * -2) = 13(z + 1) -5 + 30z + (-10 + -2z) = 13(z + 1) Reorder the terms: -5 + -10 + 30z + -2z = 13(z + 1) Combine like terms: -5 + -10 = -15 -15 + 30z + -2z = 13(z + 1) Combine like terms: 30z + -2z = 28z -15 + 28z = 13(z + 1) Reorder the terms: -15 + 28z = 13(1 + z) -15 + 28z = (1 * 13 + z * 13) -15 + 28z = (13 + 13z) Solving -15 + 28z = 13 + 13z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-13z' to each side of the equation. -15 + 28z + -13z = 13 + 13z + -13z Combine like terms: 28z + -13z = 15z -15 + 15z = 13 + 13z + -13z Combine like terms: 13z + -13z = 0 -15 + 15z = 13 + 0 -15 + 15z = 13 Add '15' to each side of the equation. -15 + 15 + 15z = 13 + 15 Combine like terms: -15 + 15 = 0 0 + 15z = 13 + 15 15z = 13 + 15 Combine like terms: 13 + 15 = 28 15z = 28 Divide each side by '15'. z = 1.866666667 Simplifying z = 1.866666667
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