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Simplifying 0.5 + 4 = 0.1(p + 8) + 0.4(p + 1) Combine like terms: 0.5 + 4 = 4.5 4.5 = 0.1(p + 8) + 0.4(p + 1) Reorder the terms: 4.5 = 0.1(8 + p) + 0.4(p + 1) 4.5 = (8 * 0.1 + p * 0.1) + 0.4(p + 1) 4.5 = (0.8 + 0.1p) + 0.4(p + 1) Reorder the terms: 4.5 = 0.8 + 0.1p + 0.4(1 + p) 4.5 = 0.8 + 0.1p + (1 * 0.4 + p * 0.4) 4.5 = 0.8 + 0.1p + (0.4 + 0.4p) Reorder the terms: 4.5 = 0.8 + 0.4 + 0.1p + 0.4p Combine like terms: 0.8 + 0.4 = 1.2 4.5 = 1.2 + 0.1p + 0.4p Combine like terms: 0.1p + 0.4p = 0.5p 4.5 = 1.2 + 0.5p Solving 4.5 = 1.2 + 0.5p Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.5p' to each side of the equation. 4.5 + -0.5p = 1.2 + 0.5p + -0.5p Combine like terms: 0.5p + -0.5p = 0.0 4.5 + -0.5p = 1.2 + 0.0 4.5 + -0.5p = 1.2 Add '-4.5' to each side of the equation. 4.5 + -4.5 + -0.5p = 1.2 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + -0.5p = 1.2 + -4.5 -0.5p = 1.2 + -4.5 Combine like terms: 1.2 + -4.5 = -3.3 -0.5p = -3.3 Divide each side by '-0.5'. p = 6.6 Simplifying p = 6.6
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