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Simplifying 5 + 12z + -2 = 8z + 31 + -3z Reorder the terms: 5 + -2 + 12z = 8z + 31 + -3z Combine like terms: 5 + -2 = 3 3 + 12z = 8z + 31 + -3z Reorder the terms: 3 + 12z = 31 + 8z + -3z Combine like terms: 8z + -3z = 5z 3 + 12z = 31 + 5z Solving 3 + 12z = 31 + 5z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-5z' to each side of the equation. 3 + 12z + -5z = 31 + 5z + -5z Combine like terms: 12z + -5z = 7z 3 + 7z = 31 + 5z + -5z Combine like terms: 5z + -5z = 0 3 + 7z = 31 + 0 3 + 7z = 31 Add '-3' to each side of the equation. 3 + -3 + 7z = 31 + -3 Combine like terms: 3 + -3 = 0 0 + 7z = 31 + -3 7z = 31 + -3 Combine like terms: 31 + -3 = 28 7z = 28 Divide each side by '7'. z = 4 Simplifying z = 4
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