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Simplifying 5p + -2(p + 1) + 3(p + -6) = 3 + -1(p + 2) Reorder the terms: 5p + -2(1 + p) + 3(p + -6) = 3 + -1(p + 2) 5p + (1 * -2 + p * -2) + 3(p + -6) = 3 + -1(p + 2) 5p + (-2 + -2p) + 3(p + -6) = 3 + -1(p + 2) Reorder the terms: 5p + -2 + -2p + 3(-6 + p) = 3 + -1(p + 2) 5p + -2 + -2p + (-6 * 3 + p * 3) = 3 + -1(p + 2) 5p + -2 + -2p + (-18 + 3p) = 3 + -1(p + 2) Reorder the terms: -2 + -18 + 5p + -2p + 3p = 3 + -1(p + 2) Combine like terms: -2 + -18 = -20 -20 + 5p + -2p + 3p = 3 + -1(p + 2) Combine like terms: 5p + -2p = 3p -20 + 3p + 3p = 3 + -1(p + 2) Combine like terms: 3p + 3p = 6p -20 + 6p = 3 + -1(p + 2) Reorder the terms: -20 + 6p = 3 + -1(2 + p) -20 + 6p = 3 + (2 * -1 + p * -1) -20 + 6p = 3 + (-2 + -1p) Combine like terms: 3 + -2 = 1 -20 + 6p = 1 + -1p Solving -20 + 6p = 1 + -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. -20 + 6p + p = 1 + -1p + p Combine like terms: 6p + p = 7p -20 + 7p = 1 + -1p + p Combine like terms: -1p + p = 0 -20 + 7p = 1 + 0 -20 + 7p = 1 Add '20' to each side of the equation. -20 + 20 + 7p = 1 + 20 Combine like terms: -20 + 20 = 0 0 + 7p = 1 + 20 7p = 1 + 20 Combine like terms: 1 + 20 = 21 7p = 21 Divide each side by '7'. p = 3 Simplifying p = 3
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