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Simplifying 13x + 7(2x + -9) + 32 + -2(7x + -13) = 4x + -2[2(7 + -3x) + -5(x + 1)] Reorder the terms: 13x + 7(-9 + 2x) + 32 + -2(7x + -13) = 4x + -2[2(7 + -3x) + -5(x + 1)] 13x + (-9 * 7 + 2x * 7) + 32 + -2(7x + -13) = 4x + -2[2(7 + -3x) + -5(x + 1)] 13x + (-63 + 14x) + 32 + -2(7x + -13) = 4x + -2[2(7 + -3x) + -5(x + 1)] Reorder the terms: 13x + -63 + 14x + 32 + -2(-13 + 7x) = 4x + -2[2(7 + -3x) + -5(x + 1)] 13x + -63 + 14x + 32 + (-13 * -2 + 7x * -2) = 4x + -2[2(7 + -3x) + -5(x + 1)] 13x + -63 + 14x + 32 + (26 + -14x) = 4x + -2[2(7 + -3x) + -5(x + 1)] Reorder the terms: -63 + 32 + 26 + 13x + 14x + -14x = 4x + -2[2(7 + -3x) + -5(x + 1)] Combine like terms: -63 + 32 = -31 -31 + 26 + 13x + 14x + -14x = 4x + -2[2(7 + -3x) + -5(x + 1)] Combine like terms: -31 + 26 = -5 -5 + 13x + 14x + -14x = 4x + -2[2(7 + -3x) + -5(x + 1)] Combine like terms: 13x + 14x = 27x -5 + 27x + -14x = 4x + -2[2(7 + -3x) + -5(x + 1)] Combine like terms: 27x + -14x = 13x -5 + 13x = 4x + -2[2(7 + -3x) + -5(x + 1)] -5 + 13x = 4x + -2[(7 * 2 + -3x * 2) + -5(x + 1)] -5 + 13x = 4x + -2[(14 + -6x) + -5(x + 1)] Reorder the terms: -5 + 13x = 4x + -2[14 + -6x + -5(1 + x)] -5 + 13x = 4x + -2[14 + -6x + (1 * -5 + x * -5)] -5 + 13x = 4x + -2[14 + -6x + (-5 + -5x)] Reorder the terms: -5 + 13x = 4x + -2[14 + -5 + -6x + -5x] Combine like terms: 14 + -5 = 9 -5 + 13x = 4x + -2[9 + -6x + -5x] Combine like terms: -6x + -5x = -11x -5 + 13x = 4x + -2[9 + -11x] -5 + 13x = 4x + [9 * -2 + -11x * -2] -5 + 13x = 4x + [-18 + 22x] Reorder the terms: -5 + 13x = -18 + 4x + 22x Combine like terms: 4x + 22x = 26x -5 + 13x = -18 + 26x Solving -5 + 13x = -18 + 26x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-26x' to each side of the equation. -5 + 13x + -26x = -18 + 26x + -26x Combine like terms: 13x + -26x = -13x -5 + -13x = -18 + 26x + -26x Combine like terms: 26x + -26x = 0 -5 + -13x = -18 + 0 -5 + -13x = -18 Add '5' to each side of the equation. -5 + 5 + -13x = -18 + 5 Combine like terms: -5 + 5 = 0 0 + -13x = -18 + 5 -13x = -18 + 5 Combine like terms: -18 + 5 = -13 -13x = -13 Divide each side by '-13'. x = 1 Simplifying x = 1
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