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Simplifying 8(z + 2) + -2(z + -1) = 2(z + -3) + 3(z + -1) Reorder the terms: 8(2 + z) + -2(z + -1) = 2(z + -3) + 3(z + -1) (2 * 8 + z * 8) + -2(z + -1) = 2(z + -3) + 3(z + -1) (16 + 8z) + -2(z + -1) = 2(z + -3) + 3(z + -1) Reorder the terms: 16 + 8z + -2(-1 + z) = 2(z + -3) + 3(z + -1) 16 + 8z + (-1 * -2 + z * -2) = 2(z + -3) + 3(z + -1) 16 + 8z + (2 + -2z) = 2(z + -3) + 3(z + -1) Reorder the terms: 16 + 2 + 8z + -2z = 2(z + -3) + 3(z + -1) Combine like terms: 16 + 2 = 18 18 + 8z + -2z = 2(z + -3) + 3(z + -1) Combine like terms: 8z + -2z = 6z 18 + 6z = 2(z + -3) + 3(z + -1) Reorder the terms: 18 + 6z = 2(-3 + z) + 3(z + -1) 18 + 6z = (-3 * 2 + z * 2) + 3(z + -1) 18 + 6z = (-6 + 2z) + 3(z + -1) Reorder the terms: 18 + 6z = -6 + 2z + 3(-1 + z) 18 + 6z = -6 + 2z + (-1 * 3 + z * 3) 18 + 6z = -6 + 2z + (-3 + 3z) Reorder the terms: 18 + 6z = -6 + -3 + 2z + 3z Combine like terms: -6 + -3 = -9 18 + 6z = -9 + 2z + 3z Combine like terms: 2z + 3z = 5z 18 + 6z = -9 + 5z Solving 18 + 6z = -9 + 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. 18 + 6z + -5z = -9 + 5z + -5z Combine like terms: 6z + -5z = 1z 18 + 1z = -9 + 5z + -5z Combine like terms: 5z + -5z = 0 18 + 1z = -9 + 0 18 + 1z = -9 Add '-18' to each side of the equation. 18 + -18 + 1z = -9 + -18 Combine like terms: 18 + -18 = 0 0 + 1z = -9 + -18 1z = -9 + -18 Combine like terms: -9 + -18 = -27 1z = -27 Divide each side by '1'. z = -27 Simplifying z = -27
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