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Simplifying 2(3(2 + w) + -1(-1w)) = 5(w + 3) + -2(1 + -1w) 2((2 * 3 + w * 3) + -1(-1w)) = 5(w + 3) + -2(1 + -1w) 2((6 + 3w) + -1(-1w)) = 5(w + 3) + -2(1 + -1w) Remove parenthesis around (-1w) 2(6 + 3w + -1 * -1w) = 5(w + 3) + -2(1 + -1w) Multiply -1 * -1 2(6 + 3w + 1w) = 5(w + 3) + -2(1 + -1w) Combine like terms: 3w + 1w = 4w 2(6 + 4w) = 5(w + 3) + -2(1 + -1w) (6 * 2 + 4w * 2) = 5(w + 3) + -2(1 + -1w) (12 + 8w) = 5(w + 3) + -2(1 + -1w) Reorder the terms: 12 + 8w = 5(3 + w) + -2(1 + -1w) 12 + 8w = (3 * 5 + w * 5) + -2(1 + -1w) 12 + 8w = (15 + 5w) + -2(1 + -1w) 12 + 8w = 15 + 5w + (1 * -2 + -1w * -2) 12 + 8w = 15 + 5w + (-2 + 2w) Reorder the terms: 12 + 8w = 15 + -2 + 5w + 2w Combine like terms: 15 + -2 = 13 12 + 8w = 13 + 5w + 2w Combine like terms: 5w + 2w = 7w 12 + 8w = 13 + 7w Solving 12 + 8w = 13 + 7w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-7w' to each side of the equation. 12 + 8w + -7w = 13 + 7w + -7w Combine like terms: 8w + -7w = 1w 12 + 1w = 13 + 7w + -7w Combine like terms: 7w + -7w = 0 12 + 1w = 13 + 0 12 + 1w = 13 Add '-12' to each side of the equation. 12 + -12 + 1w = 13 + -12 Combine like terms: 12 + -12 = 0 0 + 1w = 13 + -12 1w = 13 + -12 Combine like terms: 13 + -12 = 1 1w = 1 Divide each side by '1'. w = 1 Simplifying w = 1
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