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Simplifying 8(x + 3) + 7(x + 2) = 5x + 6(x + 1) Reorder the terms: 8(3 + x) + 7(x + 2) = 5x + 6(x + 1) (3 * 8 + x * 8) + 7(x + 2) = 5x + 6(x + 1) (24 + 8x) + 7(x + 2) = 5x + 6(x + 1) Reorder the terms: 24 + 8x + 7(2 + x) = 5x + 6(x + 1) 24 + 8x + (2 * 7 + x * 7) = 5x + 6(x + 1) 24 + 8x + (14 + 7x) = 5x + 6(x + 1) Reorder the terms: 24 + 14 + 8x + 7x = 5x + 6(x + 1) Combine like terms: 24 + 14 = 38 38 + 8x + 7x = 5x + 6(x + 1) Combine like terms: 8x + 7x = 15x 38 + 15x = 5x + 6(x + 1) Reorder the terms: 38 + 15x = 5x + 6(1 + x) 38 + 15x = 5x + (1 * 6 + x * 6) 38 + 15x = 5x + (6 + 6x) Reorder the terms: 38 + 15x = 6 + 5x + 6x Combine like terms: 5x + 6x = 11x 38 + 15x = 6 + 11x Solving 38 + 15x = 6 + 11x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11x' to each side of the equation. 38 + 15x + -11x = 6 + 11x + -11x Combine like terms: 15x + -11x = 4x 38 + 4x = 6 + 11x + -11x Combine like terms: 11x + -11x = 0 38 + 4x = 6 + 0 38 + 4x = 6 Add '-38' to each side of the equation. 38 + -38 + 4x = 6 + -38 Combine like terms: 38 + -38 = 0 0 + 4x = 6 + -38 4x = 6 + -38 Combine like terms: 6 + -38 = -32 4x = -32 Divide each side by '4'. x = -8 Simplifying x = -8
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