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Simplifying 7(p + 1) + -13(p + -2) = 2(p + -3) + 11 Reorder the terms: 7(1 + p) + -13(p + -2) = 2(p + -3) + 11 (1 * 7 + p * 7) + -13(p + -2) = 2(p + -3) + 11 (7 + 7p) + -13(p + -2) = 2(p + -3) + 11 Reorder the terms: 7 + 7p + -13(-2 + p) = 2(p + -3) + 11 7 + 7p + (-2 * -13 + p * -13) = 2(p + -3) + 11 7 + 7p + (26 + -13p) = 2(p + -3) + 11 Reorder the terms: 7 + 26 + 7p + -13p = 2(p + -3) + 11 Combine like terms: 7 + 26 = 33 33 + 7p + -13p = 2(p + -3) + 11 Combine like terms: 7p + -13p = -6p 33 + -6p = 2(p + -3) + 11 Reorder the terms: 33 + -6p = 2(-3 + p) + 11 33 + -6p = (-3 * 2 + p * 2) + 11 33 + -6p = (-6 + 2p) + 11 Reorder the terms: 33 + -6p = -6 + 11 + 2p Combine like terms: -6 + 11 = 5 33 + -6p = 5 + 2p Solving 33 + -6p = 5 + 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. 33 + -6p + -2p = 5 + 2p + -2p Combine like terms: -6p + -2p = -8p 33 + -8p = 5 + 2p + -2p Combine like terms: 2p + -2p = 0 33 + -8p = 5 + 0 33 + -8p = 5 Add '-33' to each side of the equation. 33 + -33 + -8p = 5 + -33 Combine like terms: 33 + -33 = 0 0 + -8p = 5 + -33 -8p = 5 + -33 Combine like terms: 5 + -33 = -28 -8p = -28 Divide each side by '-8'. p = 3.5 Simplifying p = 3.5
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