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Simplifying 3(2(x + -2) + -7(2x + -3)) + -5(4(2x + -5) + -1(3x + -2)) = 6(x + 1) + 1 Reorder the terms: 3(2(-2 + x) + -7(2x + -3)) + -5(4(2x + -5) + -1(3x + -2)) = 6(x + 1) + 1 3((-2 * 2 + x * 2) + -7(2x + -3)) + -5(4(2x + -5) + -1(3x + -2)) = 6(x + 1) + 1 3((-4 + 2x) + -7(2x + -3)) + -5(4(2x + -5) + -1(3x + -2)) = 6(x + 1) + 1 Reorder the terms: 3(-4 + 2x + -7(-3 + 2x)) + -5(4(2x + -5) + -1(3x + -2)) = 6(x + 1) + 1 3(-4 + 2x + (-3 * -7 + 2x * -7)) + -5(4(2x + -5) + -1(3x + -2)) = 6(x + 1) + 1 3(-4 + 2x + (21 + -14x)) + -5(4(2x + -5) + -1(3x + -2)) = 6(x + 1) + 1 Reorder the terms: 3(-4 + 21 + 2x + -14x) + -5(4(2x + -5) + -1(3x + -2)) = 6(x + 1) + 1 Combine like terms: -4 + 21 = 17 3(17 + 2x + -14x) + -5(4(2x + -5) + -1(3x + -2)) = 6(x + 1) + 1 Combine like terms: 2x + -14x = -12x 3(17 + -12x) + -5(4(2x + -5) + -1(3x + -2)) = 6(x + 1) + 1 (17 * 3 + -12x * 3) + -5(4(2x + -5) + -1(3x + -2)) = 6(x + 1) + 1 (51 + -36x) + -5(4(2x + -5) + -1(3x + -2)) = 6(x + 1) + 1 Reorder the terms: 51 + -36x + -5(4(-5 + 2x) + -1(3x + -2)) = 6(x + 1) + 1 51 + -36x + -5((-5 * 4 + 2x * 4) + -1(3x + -2)) = 6(x + 1) + 1 51 + -36x + -5((-20 + 8x) + -1(3x + -2)) = 6(x + 1) + 1 Reorder the terms: 51 + -36x + -5(-20 + 8x + -1(-2 + 3x)) = 6(x + 1) + 1 51 + -36x + -5(-20 + 8x + (-2 * -1 + 3x * -1)) = 6(x + 1) + 1 51 + -36x + -5(-20 + 8x + (2 + -3x)) = 6(x + 1) + 1 Reorder the terms: 51 + -36x + -5(-20 + 2 + 8x + -3x) = 6(x + 1) + 1 Combine like terms: -20 + 2 = -18 51 + -36x + -5(-18 + 8x + -3x) = 6(x + 1) + 1 Combine like terms: 8x + -3x = 5x 51 + -36x + -5(-18 + 5x) = 6(x + 1) + 1 51 + -36x + (-18 * -5 + 5x * -5) = 6(x + 1) + 1 51 + -36x + (90 + -25x) = 6(x + 1) + 1 Reorder the terms: 51 + 90 + -36x + -25x = 6(x + 1) + 1 Combine like terms: 51 + 90 = 141 141 + -36x + -25x = 6(x + 1) + 1 Combine like terms: -36x + -25x = -61x 141 + -61x = 6(x + 1) + 1 Reorder the terms: 141 + -61x = 6(1 + x) + 1 141 + -61x = (1 * 6 + x * 6) + 1 141 + -61x = (6 + 6x) + 1 Reorder the terms: 141 + -61x = 6 + 1 + 6x Combine like terms: 6 + 1 = 7 141 + -61x = 7 + 6x Solving 141 + -61x = 7 + 6x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6x' to each side of the equation. 141 + -61x + -6x = 7 + 6x + -6x Combine like terms: -61x + -6x = -67x 141 + -67x = 7 + 6x + -6x Combine like terms: 6x + -6x = 0 141 + -67x = 7 + 0 141 + -67x = 7 Add '-141' to each side of the equation. 141 + -141 + -67x = 7 + -141 Combine like terms: 141 + -141 = 0 0 + -67x = 7 + -141 -67x = 7 + -141 Combine like terms: 7 + -141 = -134 -67x = -134 Divide each side by '-67'. x = 2 Simplifying x = 2
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