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Simplifying 5(2p + 3q) + -7(p + 2q) + 3(p + -1q) = 0 (2p * 5 + 3q * 5) + -7(p + 2q) + 3(p + -1q) = 0 (10p + 15q) + -7(p + 2q) + 3(p + -1q) = 0 10p + 15q + (p * -7 + 2q * -7) + 3(p + -1q) = 0 10p + 15q + (-7p + -14q) + 3(p + -1q) = 0 10p + 15q + -7p + -14q + (p * 3 + -1q * 3) = 0 10p + 15q + -7p + -14q + (3p + -3q) = 0 Reorder the terms: 10p + -7p + 3p + 15q + -14q + -3q = 0 Combine like terms: 10p + -7p = 3p 3p + 3p + 15q + -14q + -3q = 0 Combine like terms: 3p + 3p = 6p 6p + 15q + -14q + -3q = 0 Combine like terms: 15q + -14q = 1q 6p + 1q + -3q = 0 Combine like terms: 1q + -3q = -2q 6p + -2q = 0 Solving 6p + -2q = 0 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '2q' to each side of the equation. 6p + -2q + 2q = 0 + 2q Combine like terms: -2q + 2q = 0 6p + 0 = 0 + 2q 6p = 0 + 2q Remove the zero: 6p = 2q Divide each side by '6'. p = 0.3333333333q Simplifying p = 0.3333333333q
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