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Simplifying 5(x + 1) + 6(x + 2) + 7(x + 3) = 8(x + 4) + -4 Reorder the terms: 5(1 + x) + 6(x + 2) + 7(x + 3) = 8(x + 4) + -4 (1 * 5 + x * 5) + 6(x + 2) + 7(x + 3) = 8(x + 4) + -4 (5 + 5x) + 6(x + 2) + 7(x + 3) = 8(x + 4) + -4 Reorder the terms: 5 + 5x + 6(2 + x) + 7(x + 3) = 8(x + 4) + -4 5 + 5x + (2 * 6 + x * 6) + 7(x + 3) = 8(x + 4) + -4 5 + 5x + (12 + 6x) + 7(x + 3) = 8(x + 4) + -4 Reorder the terms: 5 + 5x + 12 + 6x + 7(3 + x) = 8(x + 4) + -4 5 + 5x + 12 + 6x + (3 * 7 + x * 7) = 8(x + 4) + -4 5 + 5x + 12 + 6x + (21 + 7x) = 8(x + 4) + -4 Reorder the terms: 5 + 12 + 21 + 5x + 6x + 7x = 8(x + 4) + -4 Combine like terms: 5 + 12 = 17 17 + 21 + 5x + 6x + 7x = 8(x + 4) + -4 Combine like terms: 17 + 21 = 38 38 + 5x + 6x + 7x = 8(x + 4) + -4 Combine like terms: 5x + 6x = 11x 38 + 11x + 7x = 8(x + 4) + -4 Combine like terms: 11x + 7x = 18x 38 + 18x = 8(x + 4) + -4 Reorder the terms: 38 + 18x = 8(4 + x) + -4 38 + 18x = (4 * 8 + x * 8) + -4 38 + 18x = (32 + 8x) + -4 Reorder the terms: 38 + 18x = 32 + -4 + 8x Combine like terms: 32 + -4 = 28 38 + 18x = 28 + 8x Solving 38 + 18x = 28 + 8x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8x' to each side of the equation. 38 + 18x + -8x = 28 + 8x + -8x Combine like terms: 18x + -8x = 10x 38 + 10x = 28 + 8x + -8x Combine like terms: 8x + -8x = 0 38 + 10x = 28 + 0 38 + 10x = 28 Add '-38' to each side of the equation. 38 + -38 + 10x = 28 + -38 Combine like terms: 38 + -38 = 0 0 + 10x = 28 + -38 10x = 28 + -38 Combine like terms: 28 + -38 = -10 10x = -10 Divide each side by '10'. x = -1 Simplifying x = -1
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