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Simplifying 0.5(-8p + 1) = 4p + 1 Reorder the terms: 0.5(1 + -8p) = 4p + 1 (1 * 0.5 + -8p * 0.5) = 4p + 1 (0.5 + -4p) = 4p + 1 Reorder the terms: 0.5 + -4p = 1 + 4p Solving 0.5 + -4p = 1 + 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. 0.5 + -4p + -4p = 1 + 4p + -4p Combine like terms: -4p + -4p = -8p 0.5 + -8p = 1 + 4p + -4p Combine like terms: 4p + -4p = 0 0.5 + -8p = 1 + 0 0.5 + -8p = 1 Add '-0.5' to each side of the equation. 0.5 + -0.5 + -8p = 1 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -8p = 1 + -0.5 -8p = 1 + -0.5 Combine like terms: 1 + -0.5 = 0.5 -8p = 0.5 Divide each side by '-8'. p = -0.0625 Simplifying p = -0.0625
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