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Simplifying 5p + 3q + -7(5p + -5q + 7r) = 0 5p + 3q + (5p * -7 + -5q * -7 + 7r * -7) = 0 5p + 3q + (-35p + 35q + -49r) = 0 Reorder the terms: 5p + -35p + 3q + 35q + -49r = 0 Combine like terms: 5p + -35p = -30p -30p + 3q + 35q + -49r = 0 Combine like terms: 3q + 35q = 38q -30p + 38q + -49r = 0 Solving -30p + 38q + -49r = 0 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-38q' to each side of the equation. -30p + 38q + -38q + -49r = 0 + -38q Combine like terms: 38q + -38q = 0 -30p + 0 + -49r = 0 + -38q -30p + -49r = 0 + -38q Remove the zero: -30p + -49r = -38q Add '49r' to each side of the equation. -30p + -49r + 49r = -38q + 49r Combine like terms: -49r + 49r = 0 -30p + 0 = -38q + 49r -30p = -38q + 49r Divide each side by '-30'. p = 1.266666667q + -1.633333333r Simplifying p = 1.266666667q + -1.633333333r
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