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Simplifying 5(-1p + -2) = 3(-4p + -3) + 6(p + 1) Reorder the terms: 5(-2 + -1p) = 3(-4p + -3) + 6(p + 1) (-2 * 5 + -1p * 5) = 3(-4p + -3) + 6(p + 1) (-10 + -5p) = 3(-4p + -3) + 6(p + 1) Reorder the terms: -10 + -5p = 3(-3 + -4p) + 6(p + 1) -10 + -5p = (-3 * 3 + -4p * 3) + 6(p + 1) -10 + -5p = (-9 + -12p) + 6(p + 1) Reorder the terms: -10 + -5p = -9 + -12p + 6(1 + p) -10 + -5p = -9 + -12p + (1 * 6 + p * 6) -10 + -5p = -9 + -12p + (6 + 6p) Reorder the terms: -10 + -5p = -9 + 6 + -12p + 6p Combine like terms: -9 + 6 = -3 -10 + -5p = -3 + -12p + 6p Combine like terms: -12p + 6p = -6p -10 + -5p = -3 + -6p Solving -10 + -5p = -3 + -6p Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '6p' to each side of the equation. -10 + -5p + 6p = -3 + -6p + 6p Combine like terms: -5p + 6p = 1p -10 + 1p = -3 + -6p + 6p Combine like terms: -6p + 6p = 0 -10 + 1p = -3 + 0 -10 + 1p = -3 Add '10' to each side of the equation. -10 + 10 + 1p = -3 + 10 Combine like terms: -10 + 10 = 0 0 + 1p = -3 + 10 1p = -3 + 10 Combine like terms: -3 + 10 = 7 1p = 7 Divide each side by '1'. p = 7 Simplifying p = 7
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