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Simplifying 12z + -1(5z + 8) = 3(z + -7) + 9 Reorder the terms: 12z + -1(8 + 5z) = 3(z + -7) + 9 12z + (8 * -1 + 5z * -1) = 3(z + -7) + 9 12z + (-8 + -5z) = 3(z + -7) + 9 Reorder the terms: -8 + 12z + -5z = 3(z + -7) + 9 Combine like terms: 12z + -5z = 7z -8 + 7z = 3(z + -7) + 9 Reorder the terms: -8 + 7z = 3(-7 + z) + 9 -8 + 7z = (-7 * 3 + z * 3) + 9 -8 + 7z = (-21 + 3z) + 9 Reorder the terms: -8 + 7z = -21 + 9 + 3z Combine like terms: -21 + 9 = -12 -8 + 7z = -12 + 3z Solving -8 + 7z = -12 + 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 = -12 + 3z + -3z Combine like terms: 7z + -3z = 4z -8 + 4z = -12 + 3z + -3z Combine like terms: 3z + -3z = 0 -8 + 4z = -12 + 0 -8 + 4z = -12 Add '8' to each side of the equation. -8 + 8 + 4z = -12 + 8 Combine like terms: -8 + 8 = 0 0 + 4z = -12 + 8 4z = -12 + 8 Combine like terms: -12 + 8 = -4 4z = -4 Divide each side by '4'. z = -1 Simplifying z = -1
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