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Simplifying 8(z + 3) + -2(z + -2) = 2(z + -1) + 3(z + -3) Reorder the terms: 8(3 + z) + -2(z + -2) = 2(z + -1) + 3(z + -3) (3 * 8 + z * 8) + -2(z + -2) = 2(z + -1) + 3(z + -3) (24 + 8z) + -2(z + -2) = 2(z + -1) + 3(z + -3) Reorder the terms: 24 + 8z + -2(-2 + z) = 2(z + -1) + 3(z + -3) 24 + 8z + (-2 * -2 + z * -2) = 2(z + -1) + 3(z + -3) 24 + 8z + (4 + -2z) = 2(z + -1) + 3(z + -3) Reorder the terms: 24 + 4 + 8z + -2z = 2(z + -1) + 3(z + -3) Combine like terms: 24 + 4 = 28 28 + 8z + -2z = 2(z + -1) + 3(z + -3) Combine like terms: 8z + -2z = 6z 28 + 6z = 2(z + -1) + 3(z + -3) Reorder the terms: 28 + 6z = 2(-1 + z) + 3(z + -3) 28 + 6z = (-1 * 2 + z * 2) + 3(z + -3) 28 + 6z = (-2 + 2z) + 3(z + -3) Reorder the terms: 28 + 6z = -2 + 2z + 3(-3 + z) 28 + 6z = -2 + 2z + (-3 * 3 + z * 3) 28 + 6z = -2 + 2z + (-9 + 3z) Reorder the terms: 28 + 6z = -2 + -9 + 2z + 3z Combine like terms: -2 + -9 = -11 28 + 6z = -11 + 2z + 3z Combine like terms: 2z + 3z = 5z 28 + 6z = -11 + 5z Solving 28 + 6z = -11 + 5z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-5z' to each side of the equation. 28 + 6z + -5z = -11 + 5z + -5z Combine like terms: 6z + -5z = 1z 28 + 1z = -11 + 5z + -5z Combine like terms: 5z + -5z = 0 28 + 1z = -11 + 0 28 + 1z = -11 Add '-28' to each side of the equation. 28 + -28 + 1z = -11 + -28 Combine like terms: 28 + -28 = 0 0 + 1z = -11 + -28 1z = -11 + -28 Combine like terms: -11 + -28 = -39 1z = -39 Divide each side by '1'. z = -39 Simplifying z = -39
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