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Simplifying 4w + -5w + 3(w + -7) = -4(w + 4) + 7 Reorder the terms: 4w + -5w + 3(-7 + w) = -4(w + 4) + 7 4w + -5w + (-7 * 3 + w * 3) = -4(w + 4) + 7 4w + -5w + (-21 + 3w) = -4(w + 4) + 7 Reorder the terms: -21 + 4w + -5w + 3w = -4(w + 4) + 7 Combine like terms: 4w + -5w = -1w -21 + -1w + 3w = -4(w + 4) + 7 Combine like terms: -1w + 3w = 2w -21 + 2w = -4(w + 4) + 7 Reorder the terms: -21 + 2w = -4(4 + w) + 7 -21 + 2w = (4 * -4 + w * -4) + 7 -21 + 2w = (-16 + -4w) + 7 Reorder the terms: -21 + 2w = -16 + 7 + -4w Combine like terms: -16 + 7 = -9 -21 + 2w = -9 + -4w Solving -21 + 2w = -9 + -4w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '4w' to each side of the equation. -21 + 2w + 4w = -9 + -4w + 4w Combine like terms: 2w + 4w = 6w -21 + 6w = -9 + -4w + 4w Combine like terms: -4w + 4w = 0 -21 + 6w = -9 + 0 -21 + 6w = -9 Add '21' to each side of the equation. -21 + 21 + 6w = -9 + 21 Combine like terms: -21 + 21 = 0 0 + 6w = -9 + 21 6w = -9 + 21 Combine like terms: -9 + 21 = 12 6w = 12 Divide each side by '6'. w = 2 Simplifying w = 2
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