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Simplifying -1(3z + -1) + -2(z + 9) = 7(z + 1) Reorder the terms: -1(-1 + 3z) + -2(z + 9) = 7(z + 1) (-1 * -1 + 3z * -1) + -2(z + 9) = 7(z + 1) (1 + -3z) + -2(z + 9) = 7(z + 1) Reorder the terms: 1 + -3z + -2(9 + z) = 7(z + 1) 1 + -3z + (9 * -2 + z * -2) = 7(z + 1) 1 + -3z + (-18 + -2z) = 7(z + 1) Reorder the terms: 1 + -18 + -3z + -2z = 7(z + 1) Combine like terms: 1 + -18 = -17 -17 + -3z + -2z = 7(z + 1) Combine like terms: -3z + -2z = -5z -17 + -5z = 7(z + 1) Reorder the terms: -17 + -5z = 7(1 + z) -17 + -5z = (1 * 7 + z * 7) -17 + -5z = (7 + 7z) Solving -17 + -5z = 7 + 7z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-7z' to each side of the equation. -17 + -5z + -7z = 7 + 7z + -7z Combine like terms: -5z + -7z = -12z -17 + -12z = 7 + 7z + -7z Combine like terms: 7z + -7z = 0 -17 + -12z = 7 + 0 -17 + -12z = 7 Add '17' to each side of the equation. -17 + 17 + -12z = 7 + 17 Combine like terms: -17 + 17 = 0 0 + -12z = 7 + 17 -12z = 7 + 17 Combine like terms: 7 + 17 = 24 -12z = 24 Divide each side by '-12'. z = -2 Simplifying z = -2
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