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Simplifying 15(w + 3) = 20(w) + 12(2w + -1) Reorder the terms: 15(3 + w) = 20(w) + 12(2w + -1) (3 * 15 + w * 15) = 20(w) + 12(2w + -1) (45 + 15w) = 20(w) + 12(2w + -1) Reorder the terms: 45 + 15w = 20w + 12(-1 + 2w) 45 + 15w = 20w + (-1 * 12 + 2w * 12) 45 + 15w = 20w + (-12 + 24w) Reorder the terms: 45 + 15w = -12 + 20w + 24w Combine like terms: 20w + 24w = 44w 45 + 15w = -12 + 44w Solving 45 + 15w = -12 + 44w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-44w' to each side of the equation. 45 + 15w + -44w = -12 + 44w + -44w Combine like terms: 15w + -44w = -29w 45 + -29w = -12 + 44w + -44w Combine like terms: 44w + -44w = 0 45 + -29w = -12 + 0 45 + -29w = -12 Add '-45' to each side of the equation. 45 + -45 + -29w = -12 + -45 Combine like terms: 45 + -45 = 0 0 + -29w = -12 + -45 -29w = -12 + -45 Combine like terms: -12 + -45 = -57 -29w = -57 Divide each side by '-29'. w = 1.965517241 Simplifying w = 1.965517241
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