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Simplifying 6(4z + -1) + -3(z + 7) = 14(z + 1) Reorder the terms: 6(-1 + 4z) + -3(z + 7) = 14(z + 1) (-1 * 6 + 4z * 6) + -3(z + 7) = 14(z + 1) (-6 + 24z) + -3(z + 7) = 14(z + 1) Reorder the terms: -6 + 24z + -3(7 + z) = 14(z + 1) -6 + 24z + (7 * -3 + z * -3) = 14(z + 1) -6 + 24z + (-21 + -3z) = 14(z + 1) Reorder the terms: -6 + -21 + 24z + -3z = 14(z + 1) Combine like terms: -6 + -21 = -27 -27 + 24z + -3z = 14(z + 1) Combine like terms: 24z + -3z = 21z -27 + 21z = 14(z + 1) Reorder the terms: -27 + 21z = 14(1 + z) -27 + 21z = (1 * 14 + z * 14) -27 + 21z = (14 + 14z) Solving -27 + 21z = 14 + 14z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-14z' to each side of the equation. -27 + 21z + -14z = 14 + 14z + -14z Combine like terms: 21z + -14z = 7z -27 + 7z = 14 + 14z + -14z Combine like terms: 14z + -14z = 0 -27 + 7z = 14 + 0 -27 + 7z = 14 Add '27' to each side of the equation. -27 + 27 + 7z = 14 + 27 Combine like terms: -27 + 27 = 0 0 + 7z = 14 + 27 7z = 14 + 27 Combine like terms: 14 + 27 = 41 7z = 41 Divide each side by '7'. z = 5.857142857 Simplifying z = 5.857142857
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