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Simplifying 2[p + -1(3p + 7) + 1] = 2(p + 6) Reorder the terms: 2[p + -1(7 + 3p) + 1] = 2(p + 6) 2[p + (7 * -1 + 3p * -1) + 1] = 2(p + 6) 2[p + (-7 + -3p) + 1] = 2(p + 6) Reorder the terms: 2[-7 + 1 + p + -3p] = 2(p + 6) Combine like terms: -7 + 1 = -6 2[-6 + p + -3p] = 2(p + 6) Combine like terms: p + -3p = -2p 2[-6 + -2p] = 2(p + 6) [-6 * 2 + -2p * 2] = 2(p + 6) [-12 + -4p] = 2(p + 6) Reorder the terms: -12 + -4p = 2(6 + p) -12 + -4p = (6 * 2 + p * 2) -12 + -4p = (12 + 2p) Solving -12 + -4p = 12 + 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. -12 + -4p + -2p = 12 + 2p + -2p Combine like terms: -4p + -2p = -6p -12 + -6p = 12 + 2p + -2p Combine like terms: 2p + -2p = 0 -12 + -6p = 12 + 0 -12 + -6p = 12 Add '12' to each side of the equation. -12 + 12 + -6p = 12 + 12 Combine like terms: -12 + 12 = 0 0 + -6p = 12 + 12 -6p = 12 + 12 Combine like terms: 12 + 12 = 24 -6p = 24 Divide each side by '-6'. p = -4 Simplifying p = -4
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