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Simplifying 3(6z + -1) + -2(z + 1) = 14(z + 1) Reorder the terms: 3(-1 + 6z) + -2(z + 1) = 14(z + 1) (-1 * 3 + 6z * 3) + -2(z + 1) = 14(z + 1) (-3 + 18z) + -2(z + 1) = 14(z + 1) Reorder the terms: -3 + 18z + -2(1 + z) = 14(z + 1) -3 + 18z + (1 * -2 + z * -2) = 14(z + 1) -3 + 18z + (-2 + -2z) = 14(z + 1) Reorder the terms: -3 + -2 + 18z + -2z = 14(z + 1) Combine like terms: -3 + -2 = -5 -5 + 18z + -2z = 14(z + 1) Combine like terms: 18z + -2z = 16z -5 + 16z = 14(z + 1) Reorder the terms: -5 + 16z = 14(1 + z) -5 + 16z = (1 * 14 + z * 14) -5 + 16z = (14 + 14z) Solving -5 + 16z = 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. -5 + 16z + -14z = 14 + 14z + -14z Combine like terms: 16z + -14z = 2z -5 + 2z = 14 + 14z + -14z Combine like terms: 14z + -14z = 0 -5 + 2z = 14 + 0 -5 + 2z = 14 Add '5' to each side of the equation. -5 + 5 + 2z = 14 + 5 Combine like terms: -5 + 5 = 0 0 + 2z = 14 + 5 2z = 14 + 5 Combine like terms: 14 + 5 = 19 2z = 19 Divide each side by '2'. z = 9.5 Simplifying z = 9.5
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