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Simplifying 9(0.11111111 + 0.44444444w) + 2 = 4w + 3 (0.11111111 * 9 + 0.44444444w * 9) + 2 = 4w + 3 (0.99999999 + 3.99999996w) + 2 = 4w + 3 Reorder the terms: 0.99999999 + 2 + 3.99999996w = 4w + 3 Combine like terms: 0.99999999 + 2 = 2.99999999 2.99999999 + 3.99999996w = 4w + 3 Reorder the terms: 2.99999999 + 3.99999996w = 3 + 4w Solving 2.99999999 + 3.99999996w = 3 + 4w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-4w' to each side of the equation. 2.99999999 + 3.99999996w + -4w = 3 + 4w + -4w Combine like terms: 3.99999996w + -4w = -0.00000004w 2.99999999 + -0.00000004w = 3 + 4w + -4w Combine like terms: 4w + -4w = 0 2.99999999 + -0.00000004w = 3 + 0 2.99999999 + -0.00000004w = 3 Add '-2.99999999' to each side of the equation. 2.99999999 + -2.99999999 + -0.00000004w = 3 + -2.99999999 Combine like terms: 2.99999999 + -2.99999999 = 0.00000000 0.00000000 + -0.00000004w = 3 + -2.99999999 -0.00000004w = 3 + -2.99999999 Combine like terms: 3 + -2.99999999 = 0.00000001 -0.00000004w = 0.00000001 Divide each side by '-0.00000004'. w = -0.25 Simplifying w = -0.25
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