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Simplifying 0.142(14 + -7p) + -2 = -2(0.5p + 3) + 6 (14 * 0.142 + -7p * 0.142) + -2 = -2(0.5p + 3) + 6 (1.988 + -0.994p) + -2 = -2(0.5p + 3) + 6 Reorder the terms: 1.988 + -2 + -0.994p = -2(0.5p + 3) + 6 Combine like terms: 1.988 + -2 = -0.012 -0.012 + -0.994p = -2(0.5p + 3) + 6 Reorder the terms: -0.012 + -0.994p = -2(3 + 0.5p) + 6 -0.012 + -0.994p = (3 * -2 + 0.5p * -2) + 6 -0.012 + -0.994p = (-6 + -1p) + 6 Reorder the terms: -0.012 + -0.994p = -6 + 6 + -1p Combine like terms: -6 + 6 = 0 -0.012 + -0.994p = 0 + -1p -0.012 + -0.994p = -1p Solving -0.012 + -0.994p = -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. -0.012 + -0.994p + p = -1p + p Combine like terms: -0.994p + p = 0.006p -0.012 + 0.006p = -1p + p Combine like terms: -1p + p = 0 -0.012 + 0.006p = 0 Add '0.012' to each side of the equation. -0.012 + 0.012 + 0.006p = 0 + 0.012 Combine like terms: -0.012 + 0.012 = 0.000 0.000 + 0.006p = 0 + 0.012 0.006p = 0 + 0.012 Combine like terms: 0 + 0.012 = 0.012 0.006p = 0.012 Divide each side by '0.006'. p = 2 Simplifying p = 2
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