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Simplifying 81z + 6(-22z + 91) = 63z + -91z + -75 Reorder the terms: 81z + 6(91 + -22z) = 63z + -91z + -75 81z + (91 * 6 + -22z * 6) = 63z + -91z + -75 81z + (546 + -132z) = 63z + -91z + -75 Reorder the terms: 546 + 81z + -132z = 63z + -91z + -75 Combine like terms: 81z + -132z = -51z 546 + -51z = 63z + -91z + -75 Reorder the terms: 546 + -51z = -75 + 63z + -91z Combine like terms: 63z + -91z = -28z 546 + -51z = -75 + -28z Solving 546 + -51z = -75 + -28z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '28z' to each side of the equation. 546 + -51z + 28z = -75 + -28z + 28z Combine like terms: -51z + 28z = -23z 546 + -23z = -75 + -28z + 28z Combine like terms: -28z + 28z = 0 546 + -23z = -75 + 0 546 + -23z = -75 Add '-546' to each side of the equation. 546 + -546 + -23z = -75 + -546 Combine like terms: 546 + -546 = 0 0 + -23z = -75 + -546 -23z = -75 + -546 Combine like terms: -75 + -546 = -621 -23z = -621 Divide each side by '-23'. z = 27 Simplifying z = 27
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