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Simplifying 4(w + 2) + -3(w + -5) = 8 + -6(w + 1) Reorder the terms: 4(2 + w) + -3(w + -5) = 8 + -6(w + 1) (2 * 4 + w * 4) + -3(w + -5) = 8 + -6(w + 1) (8 + 4w) + -3(w + -5) = 8 + -6(w + 1) Reorder the terms: 8 + 4w + -3(-5 + w) = 8 + -6(w + 1) 8 + 4w + (-5 * -3 + w * -3) = 8 + -6(w + 1) 8 + 4w + (15 + -3w) = 8 + -6(w + 1) Reorder the terms: 8 + 15 + 4w + -3w = 8 + -6(w + 1) Combine like terms: 8 + 15 = 23 23 + 4w + -3w = 8 + -6(w + 1) Combine like terms: 4w + -3w = 1w 23 + 1w = 8 + -6(w + 1) Reorder the terms: 23 + 1w = 8 + -6(1 + w) 23 + 1w = 8 + (1 * -6 + w * -6) 23 + 1w = 8 + (-6 + -6w) Combine like terms: 8 + -6 = 2 23 + 1w = 2 + -6w Solving 23 + 1w = 2 + -6w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '6w' to each side of the equation. 23 + 1w + 6w = 2 + -6w + 6w Combine like terms: 1w + 6w = 7w 23 + 7w = 2 + -6w + 6w Combine like terms: -6w + 6w = 0 23 + 7w = 2 + 0 23 + 7w = 2 Add '-23' to each side of the equation. 23 + -23 + 7w = 2 + -23 Combine like terms: 23 + -23 = 0 0 + 7w = 2 + -23 7w = 2 + -23 Combine like terms: 2 + -23 = -21 7w = -21 Divide each side by '7'. w = -3 Simplifying w = -3
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