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Simplifying 3(p + q) + -1(p + -1q) = 0 (p * 3 + q * 3) + -1(p + -1q) = 0 (3p + 3q) + -1(p + -1q) = 0 3p + 3q + (p * -1 + -1q * -1) = 0 3p + 3q + (-1p + 1q) = 0 Reorder the terms: 3p + -1p + 3q + 1q = 0 Combine like terms: 3p + -1p = 2p 2p + 3q + 1q = 0 Combine like terms: 3q + 1q = 4q 2p + 4q = 0 Solving 2p + 4q = 0 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-4q' to each side of the equation. 2p + 4q + -4q = 0 + -4q Combine like terms: 4q + -4q = 0 2p + 0 = 0 + -4q 2p = 0 + -4q Remove the zero: 2p = -4q Divide each side by '2'. p = -2q Simplifying p = -2q
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