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Simplifying 0.1429(14 + -7p) + -2 = -2(0.5p + 3) + 6 (14 * 0.1429 + -7p * 0.1429) + -2 = -2(0.5p + 3) + 6 (2.0006 + -1.0003p) + -2 = -2(0.5p + 3) + 6 Reorder the terms: 2.0006 + -2 + -1.0003p = -2(0.5p + 3) + 6 Combine like terms: 2.0006 + -2 = 0.0006 0.0006 + -1.0003p = -2(0.5p + 3) + 6 Reorder the terms: 0.0006 + -1.0003p = -2(3 + 0.5p) + 6 0.0006 + -1.0003p = (3 * -2 + 0.5p * -2) + 6 0.0006 + -1.0003p = (-6 + -1p) + 6 Reorder the terms: 0.0006 + -1.0003p = -6 + 6 + -1p Combine like terms: -6 + 6 = 0 0.0006 + -1.0003p = 0 + -1p 0.0006 + -1.0003p = -1p Solving 0.0006 + -1.0003p = -1p Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add 'p' to each side of the equation. 0.0006 + -1.0003p + p = -1p + p Combine like terms: -1.0003p + p = -0.0003p 0.0006 + -0.0003p = -1p + p Combine like terms: -1p + p = 0 0.0006 + -0.0003p = 0 Add '-0.0006' to each side of the equation. 0.0006 + -0.0006 + -0.0003p = 0 + -0.0006 Combine like terms: 0.0006 + -0.0006 = 0.0000 0.0000 + -0.0003p = 0 + -0.0006 -0.0003p = 0 + -0.0006 Combine like terms: 0 + -0.0006 = -0.0006 -0.0003p = -0.0006 Divide each side by '-0.0003'. p = 2 Simplifying p = 2
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