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Simplifying 1 + 3p + -4p = -4(-12p + 9) + 3(p + -5) Combine like terms: 3p + -4p = -1p 1 + -1p = -4(-12p + 9) + 3(p + -5) Reorder the terms: 1 + -1p = -4(9 + -12p) + 3(p + -5) 1 + -1p = (9 * -4 + -12p * -4) + 3(p + -5) 1 + -1p = (-36 + 48p) + 3(p + -5) Reorder the terms: 1 + -1p = -36 + 48p + 3(-5 + p) 1 + -1p = -36 + 48p + (-5 * 3 + p * 3) 1 + -1p = -36 + 48p + (-15 + 3p) Reorder the terms: 1 + -1p = -36 + -15 + 48p + 3p Combine like terms: -36 + -15 = -51 1 + -1p = -51 + 48p + 3p Combine like terms: 48p + 3p = 51p 1 + -1p = -51 + 51p Solving 1 + -1p = -51 + 51p Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-51p' to each side of the equation. 1 + -1p + -51p = -51 + 51p + -51p Combine like terms: -1p + -51p = -52p 1 + -52p = -51 + 51p + -51p Combine like terms: 51p + -51p = 0 1 + -52p = -51 + 0 1 + -52p = -51 Add '-1' to each side of the equation. 1 + -1 + -52p = -51 + -1 Combine like terms: 1 + -1 = 0 0 + -52p = -51 + -1 -52p = -51 + -1 Combine like terms: -51 + -1 = -52 -52p = -52 Divide each side by '-52'. p = 1 Simplifying p = 1
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