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Simplifying 3[2(5x + -7) + -3(4x + -6)] + -4[5(x + -1) + -7x] = 6[-4(x + 2) + 7x] Reorder the terms: 3[2(-7 + 5x) + -3(4x + -6)] + -4[5(x + -1) + -7x] = 6[-4(x + 2) + 7x] 3[(-7 * 2 + 5x * 2) + -3(4x + -6)] + -4[5(x + -1) + -7x] = 6[-4(x + 2) + 7x] 3[(-14 + 10x) + -3(4x + -6)] + -4[5(x + -1) + -7x] = 6[-4(x + 2) + 7x] Reorder the terms: 3[-14 + 10x + -3(-6 + 4x)] + -4[5(x + -1) + -7x] = 6[-4(x + 2) + 7x] 3[-14 + 10x + (-6 * -3 + 4x * -3)] + -4[5(x + -1) + -7x] = 6[-4(x + 2) + 7x] 3[-14 + 10x + (18 + -12x)] + -4[5(x + -1) + -7x] = 6[-4(x + 2) + 7x] Reorder the terms: 3[-14 + 18 + 10x + -12x] + -4[5(x + -1) + -7x] = 6[-4(x + 2) + 7x] Combine like terms: -14 + 18 = 4 3[4 + 10x + -12x] + -4[5(x + -1) + -7x] = 6[-4(x + 2) + 7x] Combine like terms: 10x + -12x = -2x 3[4 + -2x] + -4[5(x + -1) + -7x] = 6[-4(x + 2) + 7x] [4 * 3 + -2x * 3] + -4[5(x + -1) + -7x] = 6[-4(x + 2) + 7x] [12 + -6x] + -4[5(x + -1) + -7x] = 6[-4(x + 2) + 7x] Reorder the terms: 12 + -6x + -4[5(-1 + x) + -7x] = 6[-4(x + 2) + 7x] 12 + -6x + -4[(-1 * 5 + x * 5) + -7x] = 6[-4(x + 2) + 7x] 12 + -6x + -4[(-5 + 5x) + -7x] = 6[-4(x + 2) + 7x] Combine like terms: 5x + -7x = -2x 12 + -6x + -4[-5 + -2x] = 6[-4(x + 2) + 7x] 12 + -6x + [-5 * -4 + -2x * -4] = 6[-4(x + 2) + 7x] 12 + -6x + [20 + 8x] = 6[-4(x + 2) + 7x] Reorder the terms: 12 + 20 + -6x + 8x = 6[-4(x + 2) + 7x] Combine like terms: 12 + 20 = 32 32 + -6x + 8x = 6[-4(x + 2) + 7x] Combine like terms: -6x + 8x = 2x 32 + 2x = 6[-4(x + 2) + 7x] Reorder the terms: 32 + 2x = 6[-4(2 + x) + 7x] 32 + 2x = 6[(2 * -4 + x * -4) + 7x] 32 + 2x = 6[(-8 + -4x) + 7x] Combine like terms: -4x + 7x = 3x 32 + 2x = 6[-8 + 3x] 32 + 2x = [-8 * 6 + 3x * 6] 32 + 2x = [-48 + 18x] Solving 32 + 2x = -48 + 18x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18x' to each side of the equation. 32 + 2x + -18x = -48 + 18x + -18x Combine like terms: 2x + -18x = -16x 32 + -16x = -48 + 18x + -18x Combine like terms: 18x + -18x = 0 32 + -16x = -48 + 0 32 + -16x = -48 Add '-32' to each side of the equation. 32 + -32 + -16x = -48 + -32 Combine like terms: 32 + -32 = 0 0 + -16x = -48 + -32 -16x = -48 + -32 Combine like terms: -48 + -32 = -80 -16x = -80 Divide each side by '-16'. x = 5 Simplifying x = 5
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