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Simplifying 8(p + -4) + -5(2p + 3) = 4.5(2p + -13) Reorder the terms: 8(-4 + p) + -5(2p + 3) = 4.5(2p + -13) (-4 * 8 + p * 8) + -5(2p + 3) = 4.5(2p + -13) (-32 + 8p) + -5(2p + 3) = 4.5(2p + -13) Reorder the terms: -32 + 8p + -5(3 + 2p) = 4.5(2p + -13) -32 + 8p + (3 * -5 + 2p * -5) = 4.5(2p + -13) -32 + 8p + (-15 + -10p) = 4.5(2p + -13) Reorder the terms: -32 + -15 + 8p + -10p = 4.5(2p + -13) Combine like terms: -32 + -15 = -47 -47 + 8p + -10p = 4.5(2p + -13) Combine like terms: 8p + -10p = -2p -47 + -2p = 4.5(2p + -13) Reorder the terms: -47 + -2p = 4.5(-13 + 2p) -47 + -2p = (-13 * 4.5 + 2p * 4.5) -47 + -2p = (-58.5 + 9p) Solving -47 + -2p = -58.5 + 9p Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-9p' to each side of the equation. -47 + -2p + -9p = -58.5 + 9p + -9p Combine like terms: -2p + -9p = -11p -47 + -11p = -58.5 + 9p + -9p Combine like terms: 9p + -9p = 0 -47 + -11p = -58.5 + 0 -47 + -11p = -58.5 Add '47' to each side of the equation. -47 + 47 + -11p = -58.5 + 47 Combine like terms: -47 + 47 = 0 0 + -11p = -58.5 + 47 -11p = -58.5 + 47 Combine like terms: -58.5 + 47 = -11.5 -11p = -11.5 Divide each side by '-11'. p = 1.045454545 Simplifying p = 1.045454545
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