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Simplifying 6(4w + 7) = 2(10w + 31) Reorder the terms: 6(7 + 4w) = 2(10w + 31) (7 * 6 + 4w * 6) = 2(10w + 31) (42 + 24w) = 2(10w + 31) Reorder the terms: 42 + 24w = 2(31 + 10w) 42 + 24w = (31 * 2 + 10w * 2) 42 + 24w = (62 + 20w) Solving 42 + 24w = 62 + 20w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-20w' to each side of the equation. 42 + 24w + -20w = 62 + 20w + -20w Combine like terms: 24w + -20w = 4w 42 + 4w = 62 + 20w + -20w Combine like terms: 20w + -20w = 0 42 + 4w = 62 + 0 42 + 4w = 62 Add '-42' to each side of the equation. 42 + -42 + 4w = 62 + -42 Combine like terms: 42 + -42 = 0 0 + 4w = 62 + -42 4w = 62 + -42 Combine like terms: 62 + -42 = 20 4w = 20 Divide each side by '4'. w = 5 Simplifying w = 5
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