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Simplifying 3(6z + -1) + -4(z + 3) = 12(z + 1) Reorder the terms: 3(-1 + 6z) + -4(z + 3) = 12(z + 1) (-1 * 3 + 6z * 3) + -4(z + 3) = 12(z + 1) (-3 + 18z) + -4(z + 3) = 12(z + 1) Reorder the terms: -3 + 18z + -4(3 + z) = 12(z + 1) -3 + 18z + (3 * -4 + z * -4) = 12(z + 1) -3 + 18z + (-12 + -4z) = 12(z + 1) Reorder the terms: -3 + -12 + 18z + -4z = 12(z + 1) Combine like terms: -3 + -12 = -15 -15 + 18z + -4z = 12(z + 1) Combine like terms: 18z + -4z = 14z -15 + 14z = 12(z + 1) Reorder the terms: -15 + 14z = 12(1 + z) -15 + 14z = (1 * 12 + z * 12) -15 + 14z = (12 + 12z) Solving -15 + 14z = 12 + 12z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-12z' to each side of the equation. -15 + 14z + -12z = 12 + 12z + -12z Combine like terms: 14z + -12z = 2z -15 + 2z = 12 + 12z + -12z Combine like terms: 12z + -12z = 0 -15 + 2z = 12 + 0 -15 + 2z = 12 Add '15' to each side of the equation. -15 + 15 + 2z = 12 + 15 Combine like terms: -15 + 15 = 0 0 + 2z = 12 + 15 2z = 12 + 15 Combine like terms: 12 + 15 = 27 2z = 27 Divide each side by '2'. z = 13.5 Simplifying z = 13.5
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