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Simplifying 47 = 7(1 + -1p) + 4(5p + -3) 47 = (1 * 7 + -1p * 7) + 4(5p + -3) 47 = (7 + -7p) + 4(5p + -3) Reorder the terms: 47 = 7 + -7p + 4(-3 + 5p) 47 = 7 + -7p + (-3 * 4 + 5p * 4) 47 = 7 + -7p + (-12 + 20p) Reorder the terms: 47 = 7 + -12 + -7p + 20p Combine like terms: 7 + -12 = -5 47 = -5 + -7p + 20p Combine like terms: -7p + 20p = 13p 47 = -5 + 13p Solving 47 = -5 + 13p Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-13p' to each side of the equation. 47 + -13p = -5 + 13p + -13p Combine like terms: 13p + -13p = 0 47 + -13p = -5 + 0 47 + -13p = -5 Add '-47' to each side of the equation. 47 + -47 + -13p = -5 + -47 Combine like terms: 47 + -47 = 0 0 + -13p = -5 + -47 -13p = -5 + -47 Combine like terms: -5 + -47 = -52 -13p = -52 Divide each side by '-13'. p = 4 Simplifying p = 4
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