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Simplifying 0.3p + 2 = 0.2(p + 5) + 0.2(p + 1) Reorder the terms: 2 + 0.3p = 0.2(p + 5) + 0.2(p + 1) Reorder the terms: 2 + 0.3p = 0.2(5 + p) + 0.2(p + 1) 2 + 0.3p = (5 * 0.2 + p * 0.2) + 0.2(p + 1) 2 + 0.3p = (1 + 0.2p) + 0.2(p + 1) Reorder the terms: 2 + 0.3p = 1 + 0.2p + 0.2(1 + p) 2 + 0.3p = 1 + 0.2p + (1 * 0.2 + p * 0.2) 2 + 0.3p = 1 + 0.2p + (0.2 + 0.2p) Reorder the terms: 2 + 0.3p = 1 + 0.2 + 0.2p + 0.2p Combine like terms: 1 + 0.2 = 1.2 2 + 0.3p = 1.2 + 0.2p + 0.2p Combine like terms: 0.2p + 0.2p = 0.4p 2 + 0.3p = 1.2 + 0.4p Solving 2 + 0.3p = 1.2 + 0.4p Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-0.4p' to each side of the equation. 2 + 0.3p + -0.4p = 1.2 + 0.4p + -0.4p Combine like terms: 0.3p + -0.4p = -0.1p 2 + -0.1p = 1.2 + 0.4p + -0.4p Combine like terms: 0.4p + -0.4p = 0.0 2 + -0.1p = 1.2 + 0.0 2 + -0.1p = 1.2 Add '-2' to each side of the equation. 2 + -2 + -0.1p = 1.2 + -2 Combine like terms: 2 + -2 = 0 0 + -0.1p = 1.2 + -2 -0.1p = 1.2 + -2 Combine like terms: 1.2 + -2 = -0.8 -0.1p = -0.8 Divide each side by '-0.1'. p = 8 Simplifying p = 8
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