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Simplifying -7(w + 1) + -1w + -8 = 8(w + 3) + 9 Reorder the terms: -7(1 + w) + -1w + -8 = 8(w + 3) + 9 (1 * -7 + w * -7) + -1w + -8 = 8(w + 3) + 9 (-7 + -7w) + -1w + -8 = 8(w + 3) + 9 Reorder the terms: -7 + -8 + -7w + -1w = 8(w + 3) + 9 Combine like terms: -7 + -8 = -15 -15 + -7w + -1w = 8(w + 3) + 9 Combine like terms: -7w + -1w = -8w -15 + -8w = 8(w + 3) + 9 Reorder the terms: -15 + -8w = 8(3 + w) + 9 -15 + -8w = (3 * 8 + w * 8) + 9 -15 + -8w = (24 + 8w) + 9 Reorder the terms: -15 + -8w = 24 + 9 + 8w Combine like terms: 24 + 9 = 33 -15 + -8w = 33 + 8w Solving -15 + -8w = 33 + 8w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-8w' to each side of the equation. -15 + -8w + -8w = 33 + 8w + -8w Combine like terms: -8w + -8w = -16w -15 + -16w = 33 + 8w + -8w Combine like terms: 8w + -8w = 0 -15 + -16w = 33 + 0 -15 + -16w = 33 Add '15' to each side of the equation. -15 + 15 + -16w = 33 + 15 Combine like terms: -15 + 15 = 0 0 + -16w = 33 + 15 -16w = 33 + 15 Combine like terms: 33 + 15 = 48 -16w = 48 Divide each side by '-16'. w = -3 Simplifying w = -3
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