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Simplifying -38 = 4(7 + 3p) + 5(-2 + -1p) -38 = (7 * 4 + 3p * 4) + 5(-2 + -1p) -38 = (28 + 12p) + 5(-2 + -1p) -38 = 28 + 12p + (-2 * 5 + -1p * 5) -38 = 28 + 12p + (-10 + -5p) Reorder the terms: -38 = 28 + -10 + 12p + -5p Combine like terms: 28 + -10 = 18 -38 = 18 + 12p + -5p Combine like terms: 12p + -5p = 7p -38 = 18 + 7p Solving -38 = 18 + 7p Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-7p' to each side of the equation. -38 + -7p = 18 + 7p + -7p Combine like terms: 7p + -7p = 0 -38 + -7p = 18 + 0 -38 + -7p = 18 Add '38' to each side of the equation. -38 + 38 + -7p = 18 + 38 Combine like terms: -38 + 38 = 0 0 + -7p = 18 + 38 -7p = 18 + 38 Combine like terms: 18 + 38 = 56 -7p = 56 Divide each side by '-7'. p = -8 Simplifying p = -8
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