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Simplifying 7(5w + -8) + -2(4w + 6) = -3(3w + 1) + 5(-2w + -4) Reorder the terms: 7(-8 + 5w) + -2(4w + 6) = -3(3w + 1) + 5(-2w + -4) (-8 * 7 + 5w * 7) + -2(4w + 6) = -3(3w + 1) + 5(-2w + -4) (-56 + 35w) + -2(4w + 6) = -3(3w + 1) + 5(-2w + -4) Reorder the terms: -56 + 35w + -2(6 + 4w) = -3(3w + 1) + 5(-2w + -4) -56 + 35w + (6 * -2 + 4w * -2) = -3(3w + 1) + 5(-2w + -4) -56 + 35w + (-12 + -8w) = -3(3w + 1) + 5(-2w + -4) Reorder the terms: -56 + -12 + 35w + -8w = -3(3w + 1) + 5(-2w + -4) Combine like terms: -56 + -12 = -68 -68 + 35w + -8w = -3(3w + 1) + 5(-2w + -4) Combine like terms: 35w + -8w = 27w -68 + 27w = -3(3w + 1) + 5(-2w + -4) Reorder the terms: -68 + 27w = -3(1 + 3w) + 5(-2w + -4) -68 + 27w = (1 * -3 + 3w * -3) + 5(-2w + -4) -68 + 27w = (-3 + -9w) + 5(-2w + -4) Reorder the terms: -68 + 27w = -3 + -9w + 5(-4 + -2w) -68 + 27w = -3 + -9w + (-4 * 5 + -2w * 5) -68 + 27w = -3 + -9w + (-20 + -10w) Reorder the terms: -68 + 27w = -3 + -20 + -9w + -10w Combine like terms: -3 + -20 = -23 -68 + 27w = -23 + -9w + -10w Combine like terms: -9w + -10w = -19w -68 + 27w = -23 + -19w Solving -68 + 27w = -23 + -19w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '19w' to each side of the equation. -68 + 27w + 19w = -23 + -19w + 19w Combine like terms: 27w + 19w = 46w -68 + 46w = -23 + -19w + 19w Combine like terms: -19w + 19w = 0 -68 + 46w = -23 + 0 -68 + 46w = -23 Add '68' to each side of the equation. -68 + 68 + 46w = -23 + 68 Combine like terms: -68 + 68 = 0 0 + 46w = -23 + 68 46w = -23 + 68 Combine like terms: -23 + 68 = 45 46w = 45 Divide each side by '46'. w = 0.9782608696 Simplifying w = 0.9782608696
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