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Simplifying 5(2w + 3) = 3(4w + 1) + -2(3w + 2) Reorder the terms: 5(3 + 2w) = 3(4w + 1) + -2(3w + 2) (3 * 5 + 2w * 5) = 3(4w + 1) + -2(3w + 2) (15 + 10w) = 3(4w + 1) + -2(3w + 2) Reorder the terms: 15 + 10w = 3(1 + 4w) + -2(3w + 2) 15 + 10w = (1 * 3 + 4w * 3) + -2(3w + 2) 15 + 10w = (3 + 12w) + -2(3w + 2) Reorder the terms: 15 + 10w = 3 + 12w + -2(2 + 3w) 15 + 10w = 3 + 12w + (2 * -2 + 3w * -2) 15 + 10w = 3 + 12w + (-4 + -6w) Reorder the terms: 15 + 10w = 3 + -4 + 12w + -6w Combine like terms: 3 + -4 = -1 15 + 10w = -1 + 12w + -6w Combine like terms: 12w + -6w = 6w 15 + 10w = -1 + 6w Solving 15 + 10w = -1 + 6w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-6w' to each side of the equation. 15 + 10w + -6w = -1 + 6w + -6w Combine like terms: 10w + -6w = 4w 15 + 4w = -1 + 6w + -6w Combine like terms: 6w + -6w = 0 15 + 4w = -1 + 0 15 + 4w = -1 Add '-15' to each side of the equation. 15 + -15 + 4w = -1 + -15 Combine like terms: 15 + -15 = 0 0 + 4w = -1 + -15 4w = -1 + -15 Combine like terms: -1 + -15 = -16 4w = -16 Divide each side by '4'. w = -4 Simplifying w = -4
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