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Simplifying 5(6z + -1) + -4(z + 1) = 13(z + 1) Reorder the terms: 5(-1 + 6z) + -4(z + 1) = 13(z + 1) (-1 * 5 + 6z * 5) + -4(z + 1) = 13(z + 1) (-5 + 30z) + -4(z + 1) = 13(z + 1) Reorder the terms: -5 + 30z + -4(1 + z) = 13(z + 1) -5 + 30z + (1 * -4 + z * -4) = 13(z + 1) -5 + 30z + (-4 + -4z) = 13(z + 1) Reorder the terms: -5 + -4 + 30z + -4z = 13(z + 1) Combine like terms: -5 + -4 = -9 -9 + 30z + -4z = 13(z + 1) Combine like terms: 30z + -4z = 26z -9 + 26z = 13(z + 1) Reorder the terms: -9 + 26z = 13(1 + z) -9 + 26z = (1 * 13 + z * 13) -9 + 26z = (13 + 13z) Solving -9 + 26z = 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. -9 + 26z + -13z = 13 + 13z + -13z Combine like terms: 26z + -13z = 13z -9 + 13z = 13 + 13z + -13z Combine like terms: 13z + -13z = 0 -9 + 13z = 13 + 0 -9 + 13z = 13 Add '9' to each side of the equation. -9 + 9 + 13z = 13 + 9 Combine like terms: -9 + 9 = 0 0 + 13z = 13 + 9 13z = 13 + 9 Combine like terms: 13 + 9 = 22 13z = 22 Divide each side by '13'. z = 1.692307692 Simplifying z = 1.692307692
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