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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 = 44 -36 + 21x = 44 + 6x + 5x Combine like terms: 6x + 5x = 11x -36 + 21x = 44 + 11x Solving -36 + 21x = 44 + 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 = 44 + 11x + -11x Combine like terms: 21x + -11x = 10x -36 + 10x = 44 + 11x + -11x Combine like terms: 11x + -11x = 0 -36 + 10x = 44 + 0 -36 + 10x = 44 Add '36' to each side of the equation. -36 + 36 + 10x = 44 + 36 Combine like terms: -36 + 36 = 0 0 + 10x = 44 + 36 10x = 44 + 36 Combine like terms: 44 + 36 = 80 10x = 80 Divide each side by '10'. x = 8 Simplifying x = 8
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