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Simplifying 10(-1z + 5) + -7(3z + 1) = 0 Reorder the terms: 10(5 + -1z) + -7(3z + 1) = 0 (5 * 10 + -1z * 10) + -7(3z + 1) = 0 (50 + -10z) + -7(3z + 1) = 0 Reorder the terms: 50 + -10z + -7(1 + 3z) = 0 50 + -10z + (1 * -7 + 3z * -7) = 0 50 + -10z + (-7 + -21z) = 0 Reorder the terms: 50 + -7 + -10z + -21z = 0 Combine like terms: 50 + -7 = 43 43 + -10z + -21z = 0 Combine like terms: -10z + -21z = -31z 43 + -31z = 0 Solving 43 + -31z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-43' to each side of the equation. 43 + -43 + -31z = 0 + -43 Combine like terms: 43 + -43 = 0 0 + -31z = 0 + -43 -31z = 0 + -43 Combine like terms: 0 + -43 = -43 -31z = -43 Divide each side by '-31'. z = 1.387096774 Simplifying z = 1.387096774
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