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Simplifying 3w + 2x + 2y + -6(-2w + x + -5y + -3) = -32 Reorder the terms: 3w + 2x + 2y + -6(-3 + -2w + x + -5y) = -32 3w + 2x + 2y + (-3 * -6 + -2w * -6 + x * -6 + -5y * -6) = -32 3w + 2x + 2y + (18 + 12w + -6x + 30y) = -32 Reorder the terms: 18 + 3w + 12w + 2x + -6x + 2y + 30y = -32 Combine like terms: 3w + 12w = 15w 18 + 15w + 2x + -6x + 2y + 30y = -32 Combine like terms: 2x + -6x = -4x 18 + 15w + -4x + 2y + 30y = -32 Combine like terms: 2y + 30y = 32y 18 + 15w + -4x + 32y = -32 Solving 18 + 15w + -4x + 32y = -32 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + 15w + -4x + -18 + 32y = -32 + -18 Reorder the terms: 18 + -18 + 15w + -4x + 32y = -32 + -18 Combine like terms: 18 + -18 = 0 0 + 15w + -4x + 32y = -32 + -18 15w + -4x + 32y = -32 + -18 Combine like terms: -32 + -18 = -50 15w + -4x + 32y = -50 Add '4x' to each side of the equation. 15w + -4x + 4x + 32y = -50 + 4x Combine like terms: -4x + 4x = 0 15w + 0 + 32y = -50 + 4x 15w + 32y = -50 + 4x Add '-32y' to each side of the equation. 15w + 32y + -32y = -50 + 4x + -32y Combine like terms: 32y + -32y = 0 15w + 0 = -50 + 4x + -32y 15w = -50 + 4x + -32y Divide each side by '15'. w = -3.333333333 + 0.2666666667x + -2.133333333y Simplifying w = -3.333333333 + 0.2666666667x + -2.133333333y
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