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Simplifying 6(5z + -1) + -3(z + 8) = 14(z + 1) Reorder the terms: 6(-1 + 5z) + -3(z + 8) = 14(z + 1) (-1 * 6 + 5z * 6) + -3(z + 8) = 14(z + 1) (-6 + 30z) + -3(z + 8) = 14(z + 1) Reorder the terms: -6 + 30z + -3(8 + z) = 14(z + 1) -6 + 30z + (8 * -3 + z * -3) = 14(z + 1) -6 + 30z + (-24 + -3z) = 14(z + 1) Reorder the terms: -6 + -24 + 30z + -3z = 14(z + 1) Combine like terms: -6 + -24 = -30 -30 + 30z + -3z = 14(z + 1) Combine like terms: 30z + -3z = 27z -30 + 27z = 14(z + 1) Reorder the terms: -30 + 27z = 14(1 + z) -30 + 27z = (1 * 14 + z * 14) -30 + 27z = (14 + 14z) Solving -30 + 27z = 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. -30 + 27z + -14z = 14 + 14z + -14z Combine like terms: 27z + -14z = 13z -30 + 13z = 14 + 14z + -14z Combine like terms: 14z + -14z = 0 -30 + 13z = 14 + 0 -30 + 13z = 14 Add '30' to each side of the equation. -30 + 30 + 13z = 14 + 30 Combine like terms: -30 + 30 = 0 0 + 13z = 14 + 30 13z = 14 + 30 Combine like terms: 14 + 30 = 44 13z = 44 Divide each side by '13'. z = 3.384615385 Simplifying z = 3.384615385
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