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Simplifying 0.1428571(14 + -7p) + -2 = -2(0.5p + 3) + 6 (14 * 0.1428571 + -7p * 0.1428571) + -2 = -2(0.5p + 3) + 6 (1.9999994 + -0.9999997p) + -2 = -2(0.5p + 3) + 6 Reorder the terms: 1.9999994 + -2 + -0.9999997p = -2(0.5p + 3) + 6 Combine like terms: 1.9999994 + -2 = -0.0000006 -0.0000006 + -0.9999997p = -2(0.5p + 3) + 6 Reorder the terms: -0.0000006 + -0.9999997p = -2(3 + 0.5p) + 6 -0.0000006 + -0.9999997p = (3 * -2 + 0.5p * -2) + 6 -0.0000006 + -0.9999997p = (-6 + -1p) + 6 Reorder the terms: -0.0000006 + -0.9999997p = -6 + 6 + -1p Combine like terms: -6 + 6 = 0 -0.0000006 + -0.9999997p = 0 + -1p -0.0000006 + -0.9999997p = -1p Solving -0.0000006 + -0.9999997p = -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. -0.0000006 + -0.9999997p + p = -1p + p Combine like terms: -0.9999997p + p = 0.0000003p -0.0000006 + 0.0000003p = -1p + p Combine like terms: -1p + p = 0 -0.0000006 + 0.0000003p = 0 Add '0.0000006' to each side of the equation. -0.0000006 + 0.0000006 + 0.0000003p = 0 + 0.0000006 Combine like terms: -0.0000006 + 0.0000006 = 0.0000000 0.0000000 + 0.0000003p = 0 + 0.0000006 0.0000003p = 0 + 0.0000006 Combine like terms: 0 + 0.0000006 = 0.0000006 0.0000003p = 0.0000006 Divide each side by '0.0000003'. p = 2 Simplifying p = 2
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