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Simplifying 12z + -9 + -10z + 3 + -8z = z + -9 + 32 + 10 + -10 Reorder the terms: -9 + 3 + 12z + -10z + -8z = z + -9 + 32 + 10 + -10 Combine like terms: -9 + 3 = -6 -6 + 12z + -10z + -8z = z + -9 + 32 + 10 + -10 Combine like terms: 12z + -10z = 2z -6 + 2z + -8z = z + -9 + 32 + 10 + -10 Combine like terms: 2z + -8z = -6z -6 + -6z = z + -9 + 32 + 10 + -10 Reorder the terms: -6 + -6z = -9 + 32 + 10 + -10 + z Combine like terms: -9 + 32 = 23 -6 + -6z = 23 + 10 + -10 + z Combine like terms: 23 + 10 = 33 -6 + -6z = 33 + -10 + z Combine like terms: 33 + -10 = 23 -6 + -6z = 23 + z Solving -6 + -6z = 23 + z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-1z' to each side of the equation. -6 + -6z + -1z = 23 + z + -1z Combine like terms: -6z + -1z = -7z -6 + -7z = 23 + z + -1z Combine like terms: z + -1z = 0 -6 + -7z = 23 + 0 -6 + -7z = 23 Add '6' to each side of the equation. -6 + 6 + -7z = 23 + 6 Combine like terms: -6 + 6 = 0 0 + -7z = 23 + 6 -7z = 23 + 6 Combine like terms: 23 + 6 = 29 -7z = 29 Divide each side by '-7'. z = -4.142857143 Simplifying z = -4.142857143
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