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Simplifying 3(p + 5) + 4(p + -2) = 4(p + 6) Reorder the terms: 3(5 + p) + 4(p + -2) = 4(p + 6) (5 * 3 + p * 3) + 4(p + -2) = 4(p + 6) (15 + 3p) + 4(p + -2) = 4(p + 6) Reorder the terms: 15 + 3p + 4(-2 + p) = 4(p + 6) 15 + 3p + (-2 * 4 + p * 4) = 4(p + 6) 15 + 3p + (-8 + 4p) = 4(p + 6) Reorder the terms: 15 + -8 + 3p + 4p = 4(p + 6) Combine like terms: 15 + -8 = 7 7 + 3p + 4p = 4(p + 6) Combine like terms: 3p + 4p = 7p 7 + 7p = 4(p + 6) Reorder the terms: 7 + 7p = 4(6 + p) 7 + 7p = (6 * 4 + p * 4) 7 + 7p = (24 + 4p) Solving 7 + 7p = 24 + 4p Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-4p' to each side of the equation. 7 + 7p + -4p = 24 + 4p + -4p Combine like terms: 7p + -4p = 3p 7 + 3p = 24 + 4p + -4p Combine like terms: 4p + -4p = 0 7 + 3p = 24 + 0 7 + 3p = 24 Add '-7' to each side of the equation. 7 + -7 + 3p = 24 + -7 Combine like terms: 7 + -7 = 0 0 + 3p = 24 + -7 3p = 24 + -7 Combine like terms: 24 + -7 = 17 3p = 17 Divide each side by '3'. p = 5.666666667 Simplifying p = 5.666666667
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