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Simplifying 5(x + 4) + 8(2x + 2) = 6(x + 1) + 5(x + 10) Reorder the terms: 5(4 + x) + 8(2x + 2) = 6(x + 1) + 5(x + 10) (4 * 5 + x * 5) + 8(2x + 2) = 6(x + 1) + 5(x + 10) (20 + 5x) + 8(2x + 2) = 6(x + 1) + 5(x + 10) Reorder the terms: 20 + 5x + 8(2 + 2x) = 6(x + 1) + 5(x + 10) 20 + 5x + (2 * 8 + 2x * 8) = 6(x + 1) + 5(x + 10) 20 + 5x + (16 + 16x) = 6(x + 1) + 5(x + 10) Reorder the terms: 20 + 16 + 5x + 16x = 6(x + 1) + 5(x + 10) Combine like terms: 20 + 16 = 36 36 + 5x + 16x = 6(x + 1) + 5(x + 10) Combine like terms: 5x + 16x = 21x 36 + 21x = 6(x + 1) + 5(x + 10) Reorder the terms: 36 + 21x = 6(1 + x) + 5(x + 10) 36 + 21x = (1 * 6 + x * 6) + 5(x + 10) 36 + 21x = (6 + 6x) + 5(x + 10) Reorder the terms: 36 + 21x = 6 + 6x + 5(10 + x) 36 + 21x = 6 + 6x + (10 * 5 + x * 5) 36 + 21x = 6 + 6x + (50 + 5x) Reorder the terms: 36 + 21x = 6 + 50 + 6x + 5x Combine like terms: 6 + 50 = 56 36 + 21x = 56 + 6x + 5x Combine like terms: 6x + 5x = 11x 36 + 21x = 56 + 11x Solving 36 + 21x = 56 + 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. 36 + 21x + -11x = 56 + 11x + -11x Combine like terms: 21x + -11x = 10x 36 + 10x = 56 + 11x + -11x Combine like terms: 11x + -11x = 0 36 + 10x = 56 + 0 36 + 10x = 56 Add '-36' to each side of the equation. 36 + -36 + 10x = 56 + -36 Combine like terms: 36 + -36 = 0 0 + 10x = 56 + -36 10x = 56 + -36 Combine like terms: 56 + -36 = 20 10x = 20 Divide each side by '10'. x = 2 Simplifying x = 2
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