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Simplifying -1(12 + 3w) + -1(9w + -5z) = 0 (12 * -1 + 3w * -1) + -1(9w + -5z) = 0 (-12 + -3w) + -1(9w + -5z) = 0 -12 + -3w + (9w * -1 + -5z * -1) = 0 -12 + -3w + (-9w + 5z) = 0 Combine like terms: -3w + -9w = -12w -12 + -12w + 5z = 0 Solving -12 + -12w + 5z = 0 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '12' to each side of the equation. -12 + -12w + 12 + 5z = 0 + 12 Reorder the terms: -12 + 12 + -12w + 5z = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -12w + 5z = 0 + 12 -12w + 5z = 0 + 12 Combine like terms: 0 + 12 = 12 -12w + 5z = 12 Add '-5z' to each side of the equation. -12w + 5z + -5z = 12 + -5z Combine like terms: 5z + -5z = 0 -12w + 0 = 12 + -5z -12w = 12 + -5z Divide each side by '-12'. w = -1 + 0.4166666667z Simplifying w = -1 + 0.4166666667z
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