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Simplifying 7(3 + -5z) + -2(1 + -32) = 8z + -1 (3 * 7 + -5z * 7) + -2(1 + -32) = 8z + -1 (21 + -35z) + -2(1 + -32) = 8z + -1 Combine like terms: 1 + -32 = -31 21 + -35z + -2(-31) = 8z + -1 Multiply -2 * -31 21 + -35z + 62 = 8z + -1 Reorder the terms: 21 + 62 + -35z = 8z + -1 Combine like terms: 21 + 62 = 83 83 + -35z = 8z + -1 Reorder the terms: 83 + -35z = -1 + 8z Solving 83 + -35z = -1 + 8z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-8z' to each side of the equation. 83 + -35z + -8z = -1 + 8z + -8z Combine like terms: -35z + -8z = -43z 83 + -43z = -1 + 8z + -8z Combine like terms: 8z + -8z = 0 83 + -43z = -1 + 0 83 + -43z = -1 Add '-83' to each side of the equation. 83 + -83 + -43z = -1 + -83 Combine like terms: 83 + -83 = 0 0 + -43z = -1 + -83 -43z = -1 + -83 Combine like terms: -1 + -83 = -84 -43z = -84 Divide each side by '-43'. z = 1.953488372 Simplifying z = 1.953488372
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