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Simplifying 10(w + -2) + -3(4w + 6) + -5w = 2(-1w + 3) + -6(2w + 1) + -4 Reorder the terms: 10(-2 + w) + -3(4w + 6) + -5w = 2(-1w + 3) + -6(2w + 1) + -4 (-2 * 10 + w * 10) + -3(4w + 6) + -5w = 2(-1w + 3) + -6(2w + 1) + -4 (-20 + 10w) + -3(4w + 6) + -5w = 2(-1w + 3) + -6(2w + 1) + -4 Reorder the terms: -20 + 10w + -3(6 + 4w) + -5w = 2(-1w + 3) + -6(2w + 1) + -4 -20 + 10w + (6 * -3 + 4w * -3) + -5w = 2(-1w + 3) + -6(2w + 1) + -4 -20 + 10w + (-18 + -12w) + -5w = 2(-1w + 3) + -6(2w + 1) + -4 Reorder the terms: -20 + -18 + 10w + -12w + -5w = 2(-1w + 3) + -6(2w + 1) + -4 Combine like terms: -20 + -18 = -38 -38 + 10w + -12w + -5w = 2(-1w + 3) + -6(2w + 1) + -4 Combine like terms: 10w + -12w = -2w -38 + -2w + -5w = 2(-1w + 3) + -6(2w + 1) + -4 Combine like terms: -2w + -5w = -7w -38 + -7w = 2(-1w + 3) + -6(2w + 1) + -4 Reorder the terms: -38 + -7w = 2(3 + -1w) + -6(2w + 1) + -4 -38 + -7w = (3 * 2 + -1w * 2) + -6(2w + 1) + -4 -38 + -7w = (6 + -2w) + -6(2w + 1) + -4 Reorder the terms: -38 + -7w = 6 + -2w + -6(1 + 2w) + -4 -38 + -7w = 6 + -2w + (1 * -6 + 2w * -6) + -4 -38 + -7w = 6 + -2w + (-6 + -12w) + -4 Reorder the terms: -38 + -7w = 6 + -6 + -4 + -2w + -12w Combine like terms: 6 + -6 = 0 -38 + -7w = 0 + -4 + -2w + -12w -38 + -7w = -4 + -2w + -12w Combine like terms: -2w + -12w = -14w -38 + -7w = -4 + -14w Solving -38 + -7w = -4 + -14w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '14w' to each side of the equation. -38 + -7w + 14w = -4 + -14w + 14w Combine like terms: -7w + 14w = 7w -38 + 7w = -4 + -14w + 14w Combine like terms: -14w + 14w = 0 -38 + 7w = -4 + 0 -38 + 7w = -4 Add '38' to each side of the equation. -38 + 38 + 7w = -4 + 38 Combine like terms: -38 + 38 = 0 0 + 7w = -4 + 38 7w = -4 + 38 Combine like terms: -4 + 38 = 34 7w = 34 Divide each side by '7'. w = 4.857142857 Simplifying w = 4.857142857
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