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Simplifying 3[6 + -1(2w + 1)] + 7 = 2(5 + -1w) Reorder the terms: 3[6 + -1(1 + 2w)] + 7 = 2(5 + -1w) 3[6 + (1 * -1 + 2w * -1)] + 7 = 2(5 + -1w) 3[6 + (-1 + -2w)] + 7 = 2(5 + -1w) Combine like terms: 6 + -1 = 5 3[5 + -2w] + 7 = 2(5 + -1w) [5 * 3 + -2w * 3] + 7 = 2(5 + -1w) [15 + -6w] + 7 = 2(5 + -1w) Reorder the terms: 15 + 7 + -6w = 2(5 + -1w) Combine like terms: 15 + 7 = 22 22 + -6w = 2(5 + -1w) 22 + -6w = (5 * 2 + -1w * 2) 22 + -6w = (10 + -2w) Solving 22 + -6w = 10 + -2w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '2w' to each side of the equation. 22 + -6w + 2w = 10 + -2w + 2w Combine like terms: -6w + 2w = -4w 22 + -4w = 10 + -2w + 2w Combine like terms: -2w + 2w = 0 22 + -4w = 10 + 0 22 + -4w = 10 Add '-22' to each side of the equation. 22 + -22 + -4w = 10 + -22 Combine like terms: 22 + -22 = 0 0 + -4w = 10 + -22 -4w = 10 + -22 Combine like terms: 10 + -22 = -12 -4w = -12 Divide each side by '-4'. w = 3 Simplifying w = 3
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