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Simplifying 12z + -9 + -10z + 3 + -8z = 2 + -9 + 3z + 10 + -102 Reorder the terms: -9 + 3 + 12z + -10z + -8z = 2 + -9 + 3z + 10 + -102 Combine like terms: -9 + 3 = -6 -6 + 12z + -10z + -8z = 2 + -9 + 3z + 10 + -102 Combine like terms: 12z + -10z = 2z -6 + 2z + -8z = 2 + -9 + 3z + 10 + -102 Combine like terms: 2z + -8z = -6z -6 + -6z = 2 + -9 + 3z + 10 + -102 Reorder the terms: -6 + -6z = 2 + -9 + 10 + -102 + 3z Combine like terms: 2 + -9 = -7 -6 + -6z = -7 + 10 + -102 + 3z Combine like terms: -7 + 10 = 3 -6 + -6z = 3 + -102 + 3z Combine like terms: 3 + -102 = -99 -6 + -6z = -99 + 3z Solving -6 + -6z = -99 + 3z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-3z' to each side of the equation. -6 + -6z + -3z = -99 + 3z + -3z Combine like terms: -6z + -3z = -9z -6 + -9z = -99 + 3z + -3z Combine like terms: 3z + -3z = 0 -6 + -9z = -99 + 0 -6 + -9z = -99 Add '6' to each side of the equation. -6 + 6 + -9z = -99 + 6 Combine like terms: -6 + 6 = 0 0 + -9z = -99 + 6 -9z = -99 + 6 Combine like terms: -99 + 6 = -93 -9z = -93 Divide each side by '-9'. z = 10.33333333 Simplifying z = 10.33333333
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