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Simplifying 2[w + -1(2w + 12) + 7] = 2(w + 5) Reorder the terms: 2[w + -1(12 + 2w) + 7] = 2(w + 5) 2[w + (12 * -1 + 2w * -1) + 7] = 2(w + 5) 2[w + (-12 + -2w) + 7] = 2(w + 5) Reorder the terms: 2[-12 + 7 + w + -2w] = 2(w + 5) Combine like terms: -12 + 7 = -5 2[-5 + w + -2w] = 2(w + 5) Combine like terms: w + -2w = -1w 2[-5 + -1w] = 2(w + 5) [-5 * 2 + -1w * 2] = 2(w + 5) [-10 + -2w] = 2(w + 5) Reorder the terms: -10 + -2w = 2(5 + w) -10 + -2w = (5 * 2 + w * 2) -10 + -2w = (10 + 2w) Solving -10 + -2w = 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. -10 + -2w + -2w = 10 + 2w + -2w Combine like terms: -2w + -2w = -4w -10 + -4w = 10 + 2w + -2w Combine like terms: 2w + -2w = 0 -10 + -4w = 10 + 0 -10 + -4w = 10 Add '10' to each side of the equation. -10 + 10 + -4w = 10 + 10 Combine like terms: -10 + 10 = 0 0 + -4w = 10 + 10 -4w = 10 + 10 Combine like terms: 10 + 10 = 20 -4w = 20 Divide each side by '-4'. w = -5 Simplifying w = -5
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