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Simplifying 3(4p + -5) + -1(p + 1) = 4 + -1(p + -4) Reorder the terms: 3(-5 + 4p) + -1(p + 1) = 4 + -1(p + -4) (-5 * 3 + 4p * 3) + -1(p + 1) = 4 + -1(p + -4) (-15 + 12p) + -1(p + 1) = 4 + -1(p + -4) Reorder the terms: -15 + 12p + -1(1 + p) = 4 + -1(p + -4) -15 + 12p + (1 * -1 + p * -1) = 4 + -1(p + -4) -15 + 12p + (-1 + -1p) = 4 + -1(p + -4) Reorder the terms: -15 + -1 + 12p + -1p = 4 + -1(p + -4) Combine like terms: -15 + -1 = -16 -16 + 12p + -1p = 4 + -1(p + -4) Combine like terms: 12p + -1p = 11p -16 + 11p = 4 + -1(p + -4) Reorder the terms: -16 + 11p = 4 + -1(-4 + p) -16 + 11p = 4 + (-4 * -1 + p * -1) -16 + 11p = 4 + (4 + -1p) Combine like terms: 4 + 4 = 8 -16 + 11p = 8 + -1p Solving -16 + 11p = 8 + -1p Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add 'p' to each side of the equation. -16 + 11p + p = 8 + -1p + p Combine like terms: 11p + p = 12p -16 + 12p = 8 + -1p + p Combine like terms: -1p + p = 0 -16 + 12p = 8 + 0 -16 + 12p = 8 Add '16' to each side of the equation. -16 + 16 + 12p = 8 + 16 Combine like terms: -16 + 16 = 0 0 + 12p = 8 + 16 12p = 8 + 16 Combine like terms: 8 + 16 = 24 12p = 24 Divide each side by '12'. p = 2 Simplifying p = 2
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