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Simplifying 6(5z + -1) + -4(z + 2) = 15(z + 1) Reorder the terms: 6(-1 + 5z) + -4(z + 2) = 15(z + 1) (-1 * 6 + 5z * 6) + -4(z + 2) = 15(z + 1) (-6 + 30z) + -4(z + 2) = 15(z + 1) Reorder the terms: -6 + 30z + -4(2 + z) = 15(z + 1) -6 + 30z + (2 * -4 + z * -4) = 15(z + 1) -6 + 30z + (-8 + -4z) = 15(z + 1) Reorder the terms: -6 + -8 + 30z + -4z = 15(z + 1) Combine like terms: -6 + -8 = -14 -14 + 30z + -4z = 15(z + 1) Combine like terms: 30z + -4z = 26z -14 + 26z = 15(z + 1) Reorder the terms: -14 + 26z = 15(1 + z) -14 + 26z = (1 * 15 + z * 15) -14 + 26z = (15 + 15z) Solving -14 + 26z = 15 + 15z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-15z' to each side of the equation. -14 + 26z + -15z = 15 + 15z + -15z Combine like terms: 26z + -15z = 11z -14 + 11z = 15 + 15z + -15z Combine like terms: 15z + -15z = 0 -14 + 11z = 15 + 0 -14 + 11z = 15 Add '14' to each side of the equation. -14 + 14 + 11z = 15 + 14 Combine like terms: -14 + 14 = 0 0 + 11z = 15 + 14 11z = 15 + 14 Combine like terms: 15 + 14 = 29 11z = 29 Divide each side by '11'. z = 2.636363636 Simplifying z = 2.636363636
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