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Simplifying 6(5z + -1) + -4(z + 7) = 9(z + 1) Reorder the terms: 6(-1 + 5z) + -4(z + 7) = 9(z + 1) (-1 * 6 + 5z * 6) + -4(z + 7) = 9(z + 1) (-6 + 30z) + -4(z + 7) = 9(z + 1) Reorder the terms: -6 + 30z + -4(7 + z) = 9(z + 1) -6 + 30z + (7 * -4 + z * -4) = 9(z + 1) -6 + 30z + (-28 + -4z) = 9(z + 1) Reorder the terms: -6 + -28 + 30z + -4z = 9(z + 1) Combine like terms: -6 + -28 = -34 -34 + 30z + -4z = 9(z + 1) Combine like terms: 30z + -4z = 26z -34 + 26z = 9(z + 1) Reorder the terms: -34 + 26z = 9(1 + z) -34 + 26z = (1 * 9 + z * 9) -34 + 26z = (9 + 9z) Solving -34 + 26z = 9 + 9z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-9z' to each side of the equation. -34 + 26z + -9z = 9 + 9z + -9z Combine like terms: 26z + -9z = 17z -34 + 17z = 9 + 9z + -9z Combine like terms: 9z + -9z = 0 -34 + 17z = 9 + 0 -34 + 17z = 9 Add '34' to each side of the equation. -34 + 34 + 17z = 9 + 34 Combine like terms: -34 + 34 = 0 0 + 17z = 9 + 34 17z = 9 + 34 Combine like terms: 9 + 34 = 43 17z = 43 Divide each side by '17'. z = 2.529411765 Simplifying z = 2.529411765
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