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Simplifying -1 + -5z + -7 + 12z = z + z + 15 + z + 1 Reorder the terms: -1 + -7 + -5z + 12z = z + z + 15 + z + 1 Combine like terms: -1 + -7 = -8 -8 + -5z + 12z = z + z + 15 + z + 1 Combine like terms: -5z + 12z = 7z -8 + 7z = z + z + 15 + z + 1 Reorder the terms: -8 + 7z = 15 + 1 + z + z + z Combine like terms: 15 + 1 = 16 -8 + 7z = 16 + z + z + z Combine like terms: z + z = 2z -8 + 7z = 16 + 2z + z Combine like terms: 2z + z = 3z -8 + 7z = 16 + 3z Solving -8 + 7z = 16 + 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. -8 + 7z + -3z = 16 + 3z + -3z Combine like terms: 7z + -3z = 4z -8 + 4z = 16 + 3z + -3z Combine like terms: 3z + -3z = 0 -8 + 4z = 16 + 0 -8 + 4z = 16 Add '8' to each side of the equation. -8 + 8 + 4z = 16 + 8 Combine like terms: -8 + 8 = 0 0 + 4z = 16 + 8 4z = 16 + 8 Combine like terms: 16 + 8 = 24 4z = 24 Divide each side by '4'. z = 6 Simplifying z = 6
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