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Simplifying 7 = 7(p + 1) + -2(3 + 5p) Reorder the terms: 7 = 7(1 + p) + -2(3 + 5p) 7 = (1 * 7 + p * 7) + -2(3 + 5p) 7 = (7 + 7p) + -2(3 + 5p) 7 = 7 + 7p + (3 * -2 + 5p * -2) 7 = 7 + 7p + (-6 + -10p) Reorder the terms: 7 = 7 + -6 + 7p + -10p Combine like terms: 7 + -6 = 1 7 = 1 + 7p + -10p Combine like terms: 7p + -10p = -3p 7 = 1 + -3p Solving 7 = 1 + -3p Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '3p' to each side of the equation. 7 + 3p = 1 + -3p + 3p Combine like terms: -3p + 3p = 0 7 + 3p = 1 + 0 7 + 3p = 1 Add '-7' to each side of the equation. 7 + -7 + 3p = 1 + -7 Combine like terms: 7 + -7 = 0 0 + 3p = 1 + -7 3p = 1 + -7 Combine like terms: 1 + -7 = -6 3p = -6 Divide each side by '3'. p = -2 Simplifying p = -2
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