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Simplifying 7m + -1[8x + -1(6n + -1p)] + -1(3m + -4n) = (10n + x) + -1[11x + -1(4m + p)] 7m + -1[8x + (6n * -1 + -1p * -1)] + -1(3m + -4n) = (10n + x) + -1[11x + -1(4m + p)] 7m + -1[8x + (-6n + 1p)] + -1(3m + -4n) = (10n + x) + -1[11x + -1(4m + p)] Reorder the terms: 7m + -1[-6n + 1p + 8x] + -1(3m + -4n) = (10n + x) + -1[11x + -1(4m + p)] 7m + [-6n * -1 + 1p * -1 + 8x * -1] + -1(3m + -4n) = (10n + x) + -1[11x + -1(4m + p)] 7m + [6n + -1p + -8x] + -1(3m + -4n) = (10n + x) + -1[11x + -1(4m + p)] 7m + 6n + -1p + -8x + (3m * -1 + -4n * -1) = (10n + x) + -1[11x + -1(4m + p)] 7m + 6n + -1p + -8x + (-3m + 4n) = (10n + x) + -1[11x + -1(4m + p)] Reorder the terms: 7m + -3m + 6n + 4n + -1p + -8x = (10n + x) + -1[11x + -1(4m + p)] Combine like terms: 7m + -3m = 4m 4m + 6n + 4n + -1p + -8x = (10n + x) + -1[11x + -1(4m + p)] Combine like terms: 6n + 4n = 10n 4m + 10n + -1p + -8x = (10n + x) + -1[11x + -1(4m + p)] Remove parenthesis around (10n + x) 4m + 10n + -1p + -8x = 10n + x + -1[11x + -1(4m + p)] 4m + 10n + -1p + -8x = 10n + x + -1[11x + (4m * -1 + p * -1)] 4m + 10n + -1p + -8x = 10n + x + -1[11x + (-4m + -1p)] Reorder the terms: 4m + 10n + -1p + -8x = 10n + x + -1[-4m + -1p + 11x] 4m + 10n + -1p + -8x = 10n + x + [-4m * -1 + -1p * -1 + 11x * -1] 4m + 10n + -1p + -8x = 10n + x + [4m + 1p + -11x] Reorder the terms: 4m + 10n + -1p + -8x = 4m + 10n + 1p + x + -11x Combine like terms: x + -11x = -10x 4m + 10n + -1p + -8x = 4m + 10n + 1p + -10x Add '-4m' to each side of the equation. 4m + 10n + -1p + -4m + -8x = 4m + 10n + 1p + -4m + -10x Reorder the terms: 4m + -4m + 10n + -1p + -8x = 4m + 10n + 1p + -4m + -10x Combine like terms: 4m + -4m = 0 0 + 10n + -1p + -8x = 4m + 10n + 1p + -4m + -10x 10n + -1p + -8x = 4m + 10n + 1p + -4m + -10x Reorder the terms: 10n + -1p + -8x = 4m + -4m + 10n + 1p + -10x Combine like terms: 4m + -4m = 0 10n + -1p + -8x = 0 + 10n + 1p + -10x 10n + -1p + -8x = 10n + 1p + -10x Add '-10n' to each side of the equation. 10n + -1p + -10n + -8x = 10n + 1p + -10n + -10x Reorder the terms: 10n + -10n + -1p + -8x = 10n + 1p + -10n + -10x Combine like terms: 10n + -10n = 0 0 + -1p + -8x = 10n + 1p + -10n + -10x -1p + -8x = 10n + 1p + -10n + -10x Reorder the terms: -1p + -8x = 10n + -10n + 1p + -10x Combine like terms: 10n + -10n = 0 -1p + -8x = 0 + 1p + -10x -1p + -8x = 1p + -10x Solving -1p + -8x = 1p + -10x Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-1p' to each side of the equation. -1p + -1p + -8x = 1p + -1p + -10x Combine like terms: -1p + -1p = -2p -2p + -8x = 1p + -1p + -10x Combine like terms: 1p + -1p = 0 -2p + -8x = 0 + -10x -2p + -8x = -10x Add '8x' to each side of the equation. -2p + -8x + 8x = -10x + 8x Combine like terms: -8x + 8x = 0 -2p + 0 = -10x + 8x -2p = -10x + 8x Combine like terms: -10x + 8x = -2x -2p = -2x Divide each side by '-2'. p = x Simplifying p = x
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