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Simplifying 2w + -7(3w + 1) = 5(5 + -3w) Reorder the terms: 2w + -7(1 + 3w) = 5(5 + -3w) 2w + (1 * -7 + 3w * -7) = 5(5 + -3w) 2w + (-7 + -21w) = 5(5 + -3w) Reorder the terms: -7 + 2w + -21w = 5(5 + -3w) Combine like terms: 2w + -21w = -19w -7 + -19w = 5(5 + -3w) -7 + -19w = (5 * 5 + -3w * 5) -7 + -19w = (25 + -15w) Solving -7 + -19w = 25 + -15w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '15w' to each side of the equation. -7 + -19w + 15w = 25 + -15w + 15w Combine like terms: -19w + 15w = -4w -7 + -4w = 25 + -15w + 15w Combine like terms: -15w + 15w = 0 -7 + -4w = 25 + 0 -7 + -4w = 25 Add '7' to each side of the equation. -7 + 7 + -4w = 25 + 7 Combine like terms: -7 + 7 = 0 0 + -4w = 25 + 7 -4w = 25 + 7 Combine like terms: 25 + 7 = 32 -4w = 32 Divide each side by '-4'. w = -8 Simplifying w = -8
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