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Simplifying 7(w + -1) = 8w + 6 + -5(-3w + -1) Reorder the terms: 7(-1 + w) = 8w + 6 + -5(-3w + -1) (-1 * 7 + w * 7) = 8w + 6 + -5(-3w + -1) (-7 + 7w) = 8w + 6 + -5(-3w + -1) Reorder the terms: -7 + 7w = 8w + 6 + -5(-1 + -3w) -7 + 7w = 8w + 6 + (-1 * -5 + -3w * -5) -7 + 7w = 8w + 6 + (5 + 15w) Reorder the terms: -7 + 7w = 6 + 5 + 8w + 15w Combine like terms: 6 + 5 = 11 -7 + 7w = 11 + 8w + 15w Combine like terms: 8w + 15w = 23w -7 + 7w = 11 + 23w Solving -7 + 7w = 11 + 23w Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-23w' to each side of the equation. -7 + 7w + -23w = 11 + 23w + -23w Combine like terms: 7w + -23w = -16w -7 + -16w = 11 + 23w + -23w Combine like terms: 23w + -23w = 0 -7 + -16w = 11 + 0 -7 + -16w = 11 Add '7' to each side of the equation. -7 + 7 + -16w = 11 + 7 Combine like terms: -7 + 7 = 0 0 + -16w = 11 + 7 -16w = 11 + 7 Combine like terms: 11 + 7 = 18 -16w = 18 Divide each side by '-16'. w = -1.125 Simplifying w = -1.125
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