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Simplifying 6(4z + -1) + -3(z + 9) = 14(z + 1) Reorder the terms: 6(-1 + 4z) + -3(z + 9) = 14(z + 1) (-1 * 6 + 4z * 6) + -3(z + 9) = 14(z + 1) (-6 + 24z) + -3(z + 9) = 14(z + 1) Reorder the terms: -6 + 24z + -3(9 + z) = 14(z + 1) -6 + 24z + (9 * -3 + z * -3) = 14(z + 1) -6 + 24z + (-27 + -3z) = 14(z + 1) Reorder the terms: -6 + -27 + 24z + -3z = 14(z + 1) Combine like terms: -6 + -27 = -33 -33 + 24z + -3z = 14(z + 1) Combine like terms: 24z + -3z = 21z -33 + 21z = 14(z + 1) Reorder the terms: -33 + 21z = 14(1 + z) -33 + 21z = (1 * 14 + z * 14) -33 + 21z = (14 + 14z) Solving -33 + 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. -33 + 21z + -14z = 14 + 14z + -14z Combine like terms: 21z + -14z = 7z -33 + 7z = 14 + 14z + -14z Combine like terms: 14z + -14z = 0 -33 + 7z = 14 + 0 -33 + 7z = 14 Add '33' to each side of the equation. -33 + 33 + 7z = 14 + 33 Combine like terms: -33 + 33 = 0 0 + 7z = 14 + 33 7z = 14 + 33 Combine like terms: 14 + 33 = 47 7z = 47 Divide each side by '7'. z = 6.714285714 Simplifying z = 6.714285714
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