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Simplifying 7(p + 6) + 6(4 + -1p) = 3 + 7p + p + -7 Reorder the terms: 7(6 + p) + 6(4 + -1p) = 3 + 7p + p + -7 (6 * 7 + p * 7) + 6(4 + -1p) = 3 + 7p + p + -7 (42 + 7p) + 6(4 + -1p) = 3 + 7p + p + -7 42 + 7p + (4 * 6 + -1p * 6) = 3 + 7p + p + -7 42 + 7p + (24 + -6p) = 3 + 7p + p + -7 Reorder the terms: 42 + 24 + 7p + -6p = 3 + 7p + p + -7 Combine like terms: 42 + 24 = 66 66 + 7p + -6p = 3 + 7p + p + -7 Combine like terms: 7p + -6p = 1p 66 + 1p = 3 + 7p + p + -7 Reorder the terms: 66 + 1p = 3 + -7 + 7p + p Combine like terms: 3 + -7 = -4 66 + 1p = -4 + 7p + p Combine like terms: 7p + p = 8p 66 + 1p = -4 + 8p Solving 66 + 1p = -4 + 8p Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-8p' to each side of the equation. 66 + 1p + -8p = -4 + 8p + -8p Combine like terms: 1p + -8p = -7p 66 + -7p = -4 + 8p + -8p Combine like terms: 8p + -8p = 0 66 + -7p = -4 + 0 66 + -7p = -4 Add '-66' to each side of the equation. 66 + -66 + -7p = -4 + -66 Combine like terms: 66 + -66 = 0 0 + -7p = -4 + -66 -7p = -4 + -66 Combine like terms: -4 + -66 = -70 -7p = -70 Divide each side by '-7'. p = 10 Simplifying p = 10
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