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Simplifying 3(4z + -1) + -2(z + 8) = 2(z + 1) Reorder the terms: 3(-1 + 4z) + -2(z + 8) = 2(z + 1) (-1 * 3 + 4z * 3) + -2(z + 8) = 2(z + 1) (-3 + 12z) + -2(z + 8) = 2(z + 1) Reorder the terms: -3 + 12z + -2(8 + z) = 2(z + 1) -3 + 12z + (8 * -2 + z * -2) = 2(z + 1) -3 + 12z + (-16 + -2z) = 2(z + 1) Reorder the terms: -3 + -16 + 12z + -2z = 2(z + 1) Combine like terms: -3 + -16 = -19 -19 + 12z + -2z = 2(z + 1) Combine like terms: 12z + -2z = 10z -19 + 10z = 2(z + 1) Reorder the terms: -19 + 10z = 2(1 + z) -19 + 10z = (1 * 2 + z * 2) -19 + 10z = (2 + 2z) Solving -19 + 10z = 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. -19 + 10z + -2z = 2 + 2z + -2z Combine like terms: 10z + -2z = 8z -19 + 8z = 2 + 2z + -2z Combine like terms: 2z + -2z = 0 -19 + 8z = 2 + 0 -19 + 8z = 2 Add '19' to each side of the equation. -19 + 19 + 8z = 2 + 19 Combine like terms: -19 + 19 = 0 0 + 8z = 2 + 19 8z = 2 + 19 Combine like terms: 2 + 19 = 21 8z = 21 Divide each side by '8'. z = 2.625 Simplifying z = 2.625
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