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Simplifying 8z + -51z + 15 + -30z + -15z + 2z = 53z + 15 + 31z + 2z + -172 Reorder the terms: 15 + 8z + -51z + -30z + -15z + 2z = 53z + 15 + 31z + 2z + -172 Combine like terms: 8z + -51z = -43z 15 + -43z + -30z + -15z + 2z = 53z + 15 + 31z + 2z + -172 Combine like terms: -43z + -30z = -73z 15 + -73z + -15z + 2z = 53z + 15 + 31z + 2z + -172 Combine like terms: -73z + -15z = -88z 15 + -88z + 2z = 53z + 15 + 31z + 2z + -172 Combine like terms: -88z + 2z = -86z 15 + -86z = 53z + 15 + 31z + 2z + -172 Reorder the terms: 15 + -86z = 15 + -172 + 53z + 31z + 2z Combine like terms: 15 + -172 = -157 15 + -86z = -157 + 53z + 31z + 2z Combine like terms: 53z + 31z = 84z 15 + -86z = -157 + 84z + 2z Combine like terms: 84z + 2z = 86z 15 + -86z = -157 + 86z Solving 15 + -86z = -157 + 86z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-86z' to each side of the equation. 15 + -86z + -86z = -157 + 86z + -86z Combine like terms: -86z + -86z = -172z 15 + -172z = -157 + 86z + -86z Combine like terms: 86z + -86z = 0 15 + -172z = -157 + 0 15 + -172z = -157 Add '-15' to each side of the equation. 15 + -15 + -172z = -157 + -15 Combine like terms: 15 + -15 = 0 0 + -172z = -157 + -15 -172z = -157 + -15 Combine like terms: -157 + -15 = -172 -172z = -172 Divide each side by '-172'. z = 1 Simplifying z = 1
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