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Simplifying 5 + -1(-2p + -3p) + -1(-3 + 4p) = 2 + -1(p + -4) + -1(-3p + 12) Combine like terms: -2p + -3p = -5p 5 + -1(-5p) + -1(-3 + 4p) = 2 + -1(p + -4) + -1(-3p + 12) Remove parenthesis around (-5p) 5 + -1 * -5p + -1(-3 + 4p) = 2 + -1(p + -4) + -1(-3p + 12) Multiply -1 * -5 5 + 5p + -1(-3 + 4p) = 2 + -1(p + -4) + -1(-3p + 12) 5 + 5p + (-3 * -1 + 4p * -1) = 2 + -1(p + -4) + -1(-3p + 12) 5 + 5p + (3 + -4p) = 2 + -1(p + -4) + -1(-3p + 12) Reorder the terms: 5 + 3 + 5p + -4p = 2 + -1(p + -4) + -1(-3p + 12) Combine like terms: 5 + 3 = 8 8 + 5p + -4p = 2 + -1(p + -4) + -1(-3p + 12) Combine like terms: 5p + -4p = 1p 8 + 1p = 2 + -1(p + -4) + -1(-3p + 12) Reorder the terms: 8 + 1p = 2 + -1(-4 + p) + -1(-3p + 12) 8 + 1p = 2 + (-4 * -1 + p * -1) + -1(-3p + 12) 8 + 1p = 2 + (4 + -1p) + -1(-3p + 12) Reorder the terms: 8 + 1p = 2 + 4 + -1p + -1(12 + -3p) 8 + 1p = 2 + 4 + -1p + (12 * -1 + -3p * -1) 8 + 1p = 2 + 4 + -1p + (-12 + 3p) Reorder the terms: 8 + 1p = 2 + 4 + -12 + -1p + 3p Combine like terms: 2 + 4 = 6 8 + 1p = 6 + -12 + -1p + 3p Combine like terms: 6 + -12 = -6 8 + 1p = -6 + -1p + 3p Combine like terms: -1p + 3p = 2p 8 + 1p = -6 + 2p Solving 8 + 1p = -6 + 2p Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-2p' to each side of the equation. 8 + 1p + -2p = -6 + 2p + -2p Combine like terms: 1p + -2p = -1p 8 + -1p = -6 + 2p + -2p Combine like terms: 2p + -2p = 0 8 + -1p = -6 + 0 8 + -1p = -6 Add '-8' to each side of the equation. 8 + -8 + -1p = -6 + -8 Combine like terms: 8 + -8 = 0 0 + -1p = -6 + -8 -1p = -6 + -8 Combine like terms: -6 + -8 = -14 -1p = -14 Divide each side by '-1'. p = 14 Simplifying p = 14
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