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Simplifying 7(3 + -5z) + -2(1 + -3z) = 8z + -1 (3 * 7 + -5z * 7) + -2(1 + -3z) = 8z + -1 (21 + -35z) + -2(1 + -3z) = 8z + -1 21 + -35z + (1 * -2 + -3z * -2) = 8z + -1 21 + -35z + (-2 + 6z) = 8z + -1 Reorder the terms: 21 + -2 + -35z + 6z = 8z + -1 Combine like terms: 21 + -2 = 19 19 + -35z + 6z = 8z + -1 Combine like terms: -35z + 6z = -29z 19 + -29z = 8z + -1 Reorder the terms: 19 + -29z = -1 + 8z Solving 19 + -29z = -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. 19 + -29z + -8z = -1 + 8z + -8z Combine like terms: -29z + -8z = -37z 19 + -37z = -1 + 8z + -8z Combine like terms: 8z + -8z = 0 19 + -37z = -1 + 0 19 + -37z = -1 Add '-19' to each side of the equation. 19 + -19 + -37z = -1 + -19 Combine like terms: 19 + -19 = 0 0 + -37z = -1 + -19 -37z = -1 + -19 Combine like terms: -1 + -19 = -20 -37z = -20 Divide each side by '-37'. z = 0.5405405405 Simplifying z = 0.5405405405
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