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Simplifying 3(6z + -1) + -2(z + 6) = 14(z + 1) Reorder the terms: 3(-1 + 6z) + -2(z + 6) = 14(z + 1) (-1 * 3 + 6z * 3) + -2(z + 6) = 14(z + 1) (-3 + 18z) + -2(z + 6) = 14(z + 1) Reorder the terms: -3 + 18z + -2(6 + z) = 14(z + 1) -3 + 18z + (6 * -2 + z * -2) = 14(z + 1) -3 + 18z + (-12 + -2z) = 14(z + 1) Reorder the terms: -3 + -12 + 18z + -2z = 14(z + 1) Combine like terms: -3 + -12 = -15 -15 + 18z + -2z = 14(z + 1) Combine like terms: 18z + -2z = 16z -15 + 16z = 14(z + 1) Reorder the terms: -15 + 16z = 14(1 + z) -15 + 16z = (1 * 14 + z * 14) -15 + 16z = (14 + 14z) Solving -15 + 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. -15 + 16z + -14z = 14 + 14z + -14z Combine like terms: 16z + -14z = 2z -15 + 2z = 14 + 14z + -14z Combine like terms: 14z + -14z = 0 -15 + 2z = 14 + 0 -15 + 2z = 14 Add '15' to each side of the equation. -15 + 15 + 2z = 14 + 15 Combine like terms: -15 + 15 = 0 0 + 2z = 14 + 15 2z = 14 + 15 Combine like terms: 14 + 15 = 29 2z = 29 Divide each side by '2'. z = 14.5 Simplifying z = 14.5
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