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Simplifying 3(2z + -1) + -2(z + 6) = 2(z + 1) Reorder the terms: 3(-1 + 2z) + -2(z + 6) = 2(z + 1) (-1 * 3 + 2z * 3) + -2(z + 6) = 2(z + 1) (-3 + 6z) + -2(z + 6) = 2(z + 1) Reorder the terms: -3 + 6z + -2(6 + z) = 2(z + 1) -3 + 6z + (6 * -2 + z * -2) = 2(z + 1) -3 + 6z + (-12 + -2z) = 2(z + 1) Reorder the terms: -3 + -12 + 6z + -2z = 2(z + 1) Combine like terms: -3 + -12 = -15 -15 + 6z + -2z = 2(z + 1) Combine like terms: 6z + -2z = 4z -15 + 4z = 2(z + 1) Reorder the terms: -15 + 4z = 2(1 + z) -15 + 4z = (1 * 2 + z * 2) -15 + 4z = (2 + 2z) Solving -15 + 4z = 2 + 2z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2z' to each side of the equation. -15 + 4z + -2z = 2 + 2z + -2z Combine like terms: 4z + -2z = 2z -15 + 2z = 2 + 2z + -2z Combine like terms: 2z + -2z = 0 -15 + 2z = 2 + 0 -15 + 2z = 2 Add '15' to each side of the equation. -15 + 15 + 2z = 2 + 15 Combine like terms: -15 + 15 = 0 0 + 2z = 2 + 15 2z = 2 + 15 Combine like terms: 2 + 15 = 17 2z = 17 Divide each side by '2'. z = 8.5 Simplifying z = 8.5
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