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Simplifying 10p + -1(50 + -2p) = 4[10 + -1(p + -5)] 10p + (50 * -1 + -2p * -1) = 4[10 + -1(p + -5)] 10p + (-50 + 2p) = 4[10 + -1(p + -5)] Reorder the terms: -50 + 10p + 2p = 4[10 + -1(p + -5)] Combine like terms: 10p + 2p = 12p -50 + 12p = 4[10 + -1(p + -5)] Reorder the terms: -50 + 12p = 4[10 + -1(-5 + p)] -50 + 12p = 4[10 + (-5 * -1 + p * -1)] -50 + 12p = 4[10 + (5 + -1p)] Combine like terms: 10 + 5 = 15 -50 + 12p = 4[15 + -1p] -50 + 12p = [15 * 4 + -1p * 4] -50 + 12p = [60 + -4p] Solving -50 + 12p = 60 + -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. -50 + 12p + 4p = 60 + -4p + 4p Combine like terms: 12p + 4p = 16p -50 + 16p = 60 + -4p + 4p Combine like terms: -4p + 4p = 0 -50 + 16p = 60 + 0 -50 + 16p = 60 Add '50' to each side of the equation. -50 + 50 + 16p = 60 + 50 Combine like terms: -50 + 50 = 0 0 + 16p = 60 + 50 16p = 60 + 50 Combine like terms: 60 + 50 = 110 16p = 110 Divide each side by '16'. p = 6.875 Simplifying p = 6.875
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