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Simplifying 7(3p + -1q) + -5(p + -2q) = 0 (3p * 7 + -1q * 7) + -5(p + -2q) = 0 (21p + -7q) + -5(p + -2q) = 0 21p + -7q + (p * -5 + -2q * -5) = 0 21p + -7q + (-5p + 10q) = 0 Reorder the terms: 21p + -5p + -7q + 10q = 0 Combine like terms: 21p + -5p = 16p 16p + -7q + 10q = 0 Combine like terms: -7q + 10q = 3q 16p + 3q = 0 Solving 16p + 3q = 0 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-3q' to each side of the equation. 16p + 3q + -3q = 0 + -3q Combine like terms: 3q + -3q = 0 16p + 0 = 0 + -3q 16p = 0 + -3q Remove the zero: 16p = -3q Divide each side by '16'. p = -0.1875q Simplifying p = -0.1875q
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