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Simplifying 3(6z + -1) + -4(z + 9) = 7(z + 1) Reorder the terms: 3(-1 + 6z) + -4(z + 9) = 7(z + 1) (-1 * 3 + 6z * 3) + -4(z + 9) = 7(z + 1) (-3 + 18z) + -4(z + 9) = 7(z + 1) Reorder the terms: -3 + 18z + -4(9 + z) = 7(z + 1) -3 + 18z + (9 * -4 + z * -4) = 7(z + 1) -3 + 18z + (-36 + -4z) = 7(z + 1) Reorder the terms: -3 + -36 + 18z + -4z = 7(z + 1) Combine like terms: -3 + -36 = -39 -39 + 18z + -4z = 7(z + 1) Combine like terms: 18z + -4z = 14z -39 + 14z = 7(z + 1) Reorder the terms: -39 + 14z = 7(1 + z) -39 + 14z = (1 * 7 + z * 7) -39 + 14z = (7 + 7z) Solving -39 + 14z = 7 + 7z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-7z' to each side of the equation. -39 + 14z + -7z = 7 + 7z + -7z Combine like terms: 14z + -7z = 7z -39 + 7z = 7 + 7z + -7z Combine like terms: 7z + -7z = 0 -39 + 7z = 7 + 0 -39 + 7z = 7 Add '39' to each side of the equation. -39 + 39 + 7z = 7 + 39 Combine like terms: -39 + 39 = 0 0 + 7z = 7 + 39 7z = 7 + 39 Combine like terms: 7 + 39 = 46 7z = 46 Divide each side by '7'. z = 6.571428571 Simplifying z = 6.571428571
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