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Simplifying 3(6z + -1) + -2(z + 3) = 12(z + 1) Reorder the terms: 3(-1 + 6z) + -2(z + 3) = 12(z + 1) (-1 * 3 + 6z * 3) + -2(z + 3) = 12(z + 1) (-3 + 18z) + -2(z + 3) = 12(z + 1) Reorder the terms: -3 + 18z + -2(3 + z) = 12(z + 1) -3 + 18z + (3 * -2 + z * -2) = 12(z + 1) -3 + 18z + (-6 + -2z) = 12(z + 1) Reorder the terms: -3 + -6 + 18z + -2z = 12(z + 1) Combine like terms: -3 + -6 = -9 -9 + 18z + -2z = 12(z + 1) Combine like terms: 18z + -2z = 16z -9 + 16z = 12(z + 1) Reorder the terms: -9 + 16z = 12(1 + z) -9 + 16z = (1 * 12 + z * 12) -9 + 16z = (12 + 12z) Solving -9 + 16z = 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. -9 + 16z + -12z = 12 + 12z + -12z Combine like terms: 16z + -12z = 4z -9 + 4z = 12 + 12z + -12z Combine like terms: 12z + -12z = 0 -9 + 4z = 12 + 0 -9 + 4z = 12 Add '9' to each side of the equation. -9 + 9 + 4z = 12 + 9 Combine like terms: -9 + 9 = 0 0 + 4z = 12 + 9 4z = 12 + 9 Combine like terms: 12 + 9 = 21 4z = 21 Divide each side by '4'. z = 5.25 Simplifying z = 5.25
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