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Simplifying 9(z + 1) + -2(z + -1) = 3(z + -1) + 3(z + -2) Reorder the terms: 9(1 + z) + -2(z + -1) = 3(z + -1) + 3(z + -2) (1 * 9 + z * 9) + -2(z + -1) = 3(z + -1) + 3(z + -2) (9 + 9z) + -2(z + -1) = 3(z + -1) + 3(z + -2) Reorder the terms: 9 + 9z + -2(-1 + z) = 3(z + -1) + 3(z + -2) 9 + 9z + (-1 * -2 + z * -2) = 3(z + -1) + 3(z + -2) 9 + 9z + (2 + -2z) = 3(z + -1) + 3(z + -2) Reorder the terms: 9 + 2 + 9z + -2z = 3(z + -1) + 3(z + -2) Combine like terms: 9 + 2 = 11 11 + 9z + -2z = 3(z + -1) + 3(z + -2) Combine like terms: 9z + -2z = 7z 11 + 7z = 3(z + -1) + 3(z + -2) Reorder the terms: 11 + 7z = 3(-1 + z) + 3(z + -2) 11 + 7z = (-1 * 3 + z * 3) + 3(z + -2) 11 + 7z = (-3 + 3z) + 3(z + -2) Reorder the terms: 11 + 7z = -3 + 3z + 3(-2 + z) 11 + 7z = -3 + 3z + (-2 * 3 + z * 3) 11 + 7z = -3 + 3z + (-6 + 3z) Reorder the terms: 11 + 7z = -3 + -6 + 3z + 3z Combine like terms: -3 + -6 = -9 11 + 7z = -9 + 3z + 3z Combine like terms: 3z + 3z = 6z 11 + 7z = -9 + 6z Solving 11 + 7z = -9 + 6z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-6z' to each side of the equation. 11 + 7z + -6z = -9 + 6z + -6z Combine like terms: 7z + -6z = 1z 11 + 1z = -9 + 6z + -6z Combine like terms: 6z + -6z = 0 11 + 1z = -9 + 0 11 + 1z = -9 Add '-11' to each side of the equation. 11 + -11 + 1z = -9 + -11 Combine like terms: 11 + -11 = 0 0 + 1z = -9 + -11 1z = -9 + -11 Combine like terms: -9 + -11 = -20 1z = -20 Divide each side by '1'. z = -20 Simplifying z = -20
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