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Simplifying k(q + r) + -1b(q + r) + -1q + -1r = 0 (q * k + r * k) + -1b(q + r) + -1q + -1r = 0 (kq + kr) + -1b(q + r) + -1q + -1r = 0 kq + kr + (q * -1b + r * -1b) + -1q + -1r = 0 kq + kr + (-1bq + -1br) + -1q + -1r = 0 Reorder the terms: -1bq + -1br + kq + kr + -1q + -1r = 0 Solving -1bq + -1br + kq + kr + -1q + -1r = 0 Solving for variable 'b'. Move all terms containing b to the left, all other terms to the right. Add '-1kq' to each side of the equation. -1bq + -1br + kq + kr + -1q + -1kq + -1r = 0 + -1kq Reorder the terms: -1bq + -1br + kq + -1kq + kr + -1q + -1r = 0 + -1kq Combine like terms: kq + -1kq = 0 -1bq + -1br + 0 + kr + -1q + -1r = 0 + -1kq -1bq + -1br + kr + -1q + -1r = 0 + -1kq Remove the zero: -1bq + -1br + kr + -1q + -1r = -1kq Add '-1kr' to each side of the equation. -1bq + -1br + kr + -1q + -1kr + -1r = -1kq + -1kr Reorder the terms: -1bq + -1br + kr + -1kr + -1q + -1r = -1kq + -1kr Combine like terms: kr + -1kr = 0 -1bq + -1br + 0 + -1q + -1r = -1kq + -1kr -1bq + -1br + -1q + -1r = -1kq + -1kr Add 'q' to each side of the equation. -1bq + -1br + -1q + q + -1r = -1kq + -1kr + q Combine like terms: -1q + q = 0 -1bq + -1br + 0 + -1r = -1kq + -1kr + q -1bq + -1br + -1r = -1kq + -1kr + q Add 'r' to each side of the equation. -1bq + -1br + -1r + r = -1kq + -1kr + q + r Combine like terms: -1r + r = 0 -1bq + -1br + 0 = -1kq + -1kr + q + r -1bq + -1br = -1kq + -1kr + q + r Reorder the terms: -1bq + -1br + kq + kr + -1q + -1r = -1kq + kq + -1kr + kr + q + -1q + r + -1r Combine like terms: -1kq + kq = 0 -1bq + -1br + kq + kr + -1q + -1r = 0 + -1kr + kr + q + -1q + r + -1r -1bq + -1br + kq + kr + -1q + -1r = -1kr + kr + q + -1q + r + -1r Combine like terms: -1kr + kr = 0 -1bq + -1br + kq + kr + -1q + -1r = 0 + q + -1q + r + -1r -1bq + -1br + kq + kr + -1q + -1r = q + -1q + r + -1r Combine like terms: q + -1q = 0 -1bq + -1br + kq + kr + -1q + -1r = 0 + r + -1r -1bq + -1br + kq + kr + -1q + -1r = r + -1r Combine like terms: r + -1r = 0 -1bq + -1br + kq + kr + -1q + -1r = 0 The solution to this equation could not be determined.
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