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Simplifying 7(z + 3) + -2(z + -3) = 2(z + -4) + 2(z + -3) Reorder the terms: 7(3 + z) + -2(z + -3) = 2(z + -4) + 2(z + -3) (3 * 7 + z * 7) + -2(z + -3) = 2(z + -4) + 2(z + -3) (21 + 7z) + -2(z + -3) = 2(z + -4) + 2(z + -3) Reorder the terms: 21 + 7z + -2(-3 + z) = 2(z + -4) + 2(z + -3) 21 + 7z + (-3 * -2 + z * -2) = 2(z + -4) + 2(z + -3) 21 + 7z + (6 + -2z) = 2(z + -4) + 2(z + -3) Reorder the terms: 21 + 6 + 7z + -2z = 2(z + -4) + 2(z + -3) Combine like terms: 21 + 6 = 27 27 + 7z + -2z = 2(z + -4) + 2(z + -3) Combine like terms: 7z + -2z = 5z 27 + 5z = 2(z + -4) + 2(z + -3) Reorder the terms: 27 + 5z = 2(-4 + z) + 2(z + -3) 27 + 5z = (-4 * 2 + z * 2) + 2(z + -3) 27 + 5z = (-8 + 2z) + 2(z + -3) Reorder the terms: 27 + 5z = -8 + 2z + 2(-3 + z) 27 + 5z = -8 + 2z + (-3 * 2 + z * 2) 27 + 5z = -8 + 2z + (-6 + 2z) Reorder the terms: 27 + 5z = -8 + -6 + 2z + 2z Combine like terms: -8 + -6 = -14 27 + 5z = -14 + 2z + 2z Combine like terms: 2z + 2z = 4z 27 + 5z = -14 + 4z Solving 27 + 5z = -14 + 4z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4z' to each side of the equation. 27 + 5z + -4z = -14 + 4z + -4z Combine like terms: 5z + -4z = 1z 27 + 1z = -14 + 4z + -4z Combine like terms: 4z + -4z = 0 27 + 1z = -14 + 0 27 + 1z = -14 Add '-27' to each side of the equation. 27 + -27 + 1z = -14 + -27 Combine like terms: 27 + -27 = 0 0 + 1z = -14 + -27 1z = -14 + -27 Combine like terms: -14 + -27 = -41 1z = -41 Divide each side by '1'. z = -41 Simplifying z = -41
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