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Simplifying 52 = -7(p + 1) + 6(2p + 4) Reorder the terms: 52 = -7(1 + p) + 6(2p + 4) 52 = (1 * -7 + p * -7) + 6(2p + 4) 52 = (-7 + -7p) + 6(2p + 4) Reorder the terms: 52 = -7 + -7p + 6(4 + 2p) 52 = -7 + -7p + (4 * 6 + 2p * 6) 52 = -7 + -7p + (24 + 12p) Reorder the terms: 52 = -7 + 24 + -7p + 12p Combine like terms: -7 + 24 = 17 52 = 17 + -7p + 12p Combine like terms: -7p + 12p = 5p 52 = 17 + 5p Solving 52 = 17 + 5p Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-5p' to each side of the equation. 52 + -5p = 17 + 5p + -5p Combine like terms: 5p + -5p = 0 52 + -5p = 17 + 0 52 + -5p = 17 Add '-52' to each side of the equation. 52 + -52 + -5p = 17 + -52 Combine like terms: 52 + -52 = 0 0 + -5p = 17 + -52 -5p = 17 + -52 Combine like terms: 17 + -52 = -35 -5p = -35 Divide each side by '-5'. p = 7 Simplifying p = 7
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