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Simplifying 2x + z + w = 4x + 1.5z + -1w Reorder the terms: w + 2x + z = 4x + 1.5z + -1w Reorder the terms: w + 2x + z = -1w + 4x + 1.5z Solving w + 2x + z = -1w + 4x + 1.5z Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add 'w' to each side of the equation. w + 2x + w + z = -1w + 4x + w + 1.5z Reorder the terms: w + w + 2x + z = -1w + 4x + w + 1.5z Combine like terms: w + w = 2w 2w + 2x + z = -1w + 4x + w + 1.5z Reorder the terms: 2w + 2x + z = -1w + w + 4x + 1.5z Combine like terms: -1w + w = 0 2w + 2x + z = 0 + 4x + 1.5z 2w + 2x + z = 4x + 1.5z Add '-2x' to each side of the equation. 2w + 2x + -2x + z = 4x + -2x + 1.5z Combine like terms: 2x + -2x = 0 2w + 0 + z = 4x + -2x + 1.5z 2w + z = 4x + -2x + 1.5z Combine like terms: 4x + -2x = 2x 2w + z = 2x + 1.5z Add '-1z' to each side of the equation. 2w + z + -1z = 2x + 1.5z + -1z Combine like terms: z + -1z = 0 2w + 0 = 2x + 1.5z + -1z 2w = 2x + 1.5z + -1z Combine like terms: 1.5z + -1z = 0.5z 2w = 2x + 0.5z Divide each side by '2'. w = x + 0.25z Simplifying w = x + 0.25z
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