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Simplifying 20[3(x + 2)] + -7x + 9(x + 2) + 4[2(10x + -1)] = 10[9(x + 5) + 8(x + -6) + 2] Reorder the terms: 20[3(2 + x)] + -7x + 9(x + 2) + 4[2(10x + -1)] = 10[9(x + 5) + 8(x + -6) + 2] 20[(2 * 3 + x * 3)] + -7x + 9(x + 2) + 4[2(10x + -1)] = 10[9(x + 5) + 8(x + -6) + 2] 20[(6 + 3x)] + -7x + 9(x + 2) + 4[2(10x + -1)] = 10[9(x + 5) + 8(x + -6) + 2] [6 * 20 + 3x * 20] + -7x + 9(x + 2) + 4[2(10x + -1)] = 10[9(x + 5) + 8(x + -6) + 2] [120 + 60x] + -7x + 9(x + 2) + 4[2(10x + -1)] = 10[9(x + 5) + 8(x + -6) + 2] Reorder the terms: 120 + 60x + -7x + 9(2 + x) + 4[2(10x + -1)] = 10[9(x + 5) + 8(x + -6) + 2] 120 + 60x + -7x + (2 * 9 + x * 9) + 4[2(10x + -1)] = 10[9(x + 5) + 8(x + -6) + 2] 120 + 60x + -7x + (18 + 9x) + 4[2(10x + -1)] = 10[9(x + 5) + 8(x + -6) + 2] Reorder the terms: 120 + 60x + -7x + 18 + 9x + 4[2(-1 + 10x)] = 10[9(x + 5) + 8(x + -6) + 2] 120 + 60x + -7x + 18 + 9x + 4[(-1 * 2 + 10x * 2)] = 10[9(x + 5) + 8(x + -6) + 2] 120 + 60x + -7x + 18 + 9x + 4[(-2 + 20x)] = 10[9(x + 5) + 8(x + -6) + 2] 120 + 60x + -7x + 18 + 9x + [-2 * 4 + 20x * 4] = 10[9(x + 5) + 8(x + -6) + 2] 120 + 60x + -7x + 18 + 9x + [-8 + 80x] = 10[9(x + 5) + 8(x + -6) + 2] Reorder the terms: 120 + 18 + -8 + 60x + -7x + 9x + 80x = 10[9(x + 5) + 8(x + -6) + 2] Combine like terms: 120 + 18 = 138 138 + -8 + 60x + -7x + 9x + 80x = 10[9(x + 5) + 8(x + -6) + 2] Combine like terms: 138 + -8 = 130 130 + 60x + -7x + 9x + 80x = 10[9(x + 5) + 8(x + -6) + 2] Combine like terms: 60x + -7x = 53x 130 + 53x + 9x + 80x = 10[9(x + 5) + 8(x + -6) + 2] Combine like terms: 53x + 9x = 62x 130 + 62x + 80x = 10[9(x + 5) + 8(x + -6) + 2] Combine like terms: 62x + 80x = 142x 130 + 142x = 10[9(x + 5) + 8(x + -6) + 2] Reorder the terms: 130 + 142x = 10[9(5 + x) + 8(x + -6) + 2] 130 + 142x = 10[(5 * 9 + x * 9) + 8(x + -6) + 2] 130 + 142x = 10[(45 + 9x) + 8(x + -6) + 2] Reorder the terms: 130 + 142x = 10[45 + 9x + 8(-6 + x) + 2] 130 + 142x = 10[45 + 9x + (-6 * 8 + x * 8) + 2] 130 + 142x = 10[45 + 9x + (-48 + 8x) + 2] Reorder the terms: 130 + 142x = 10[45 + -48 + 2 + 9x + 8x] Combine like terms: 45 + -48 = -3 130 + 142x = 10[-3 + 2 + 9x + 8x] Combine like terms: -3 + 2 = -1 130 + 142x = 10[-1 + 9x + 8x] Combine like terms: 9x + 8x = 17x 130 + 142x = 10[-1 + 17x] 130 + 142x = [-1 * 10 + 17x * 10] 130 + 142x = [-10 + 170x] Solving 130 + 142x = -10 + 170x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-170x' to each side of the equation. 130 + 142x + -170x = -10 + 170x + -170x Combine like terms: 142x + -170x = -28x 130 + -28x = -10 + 170x + -170x Combine like terms: 170x + -170x = 0 130 + -28x = -10 + 0 130 + -28x = -10 Add '-130' to each side of the equation. 130 + -130 + -28x = -10 + -130 Combine like terms: 130 + -130 = 0 0 + -28x = -10 + -130 -28x = -10 + -130 Combine like terms: -10 + -130 = -140 -28x = -140 Divide each side by '-28'. x = 5 Simplifying x = 5
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