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Simplifying (10x + 9) * x = 8 + -1(1 + -5x)(2x + 3) Reorder the terms: (9 + 10x) * x = 8 + -1(1 + -5x)(2x + 3) Reorder the terms for easier multiplication: x(9 + 10x) = 8 + -1(1 + -5x)(2x + 3) (9 * x + 10x * x) = 8 + -1(1 + -5x)(2x + 3) (9x + 10x2) = 8 + -1(1 + -5x)(2x + 3) Reorder the terms: 9x + 10x2 = 8 + -1(1 + -5x)(3 + 2x) Multiply (1 + -5x) * (3 + 2x) 9x + 10x2 = 8 + -1(1(3 + 2x) + -5x * (3 + 2x)) 9x + 10x2 = 8 + -1((3 * 1 + 2x * 1) + -5x * (3 + 2x)) 9x + 10x2 = 8 + -1((3 + 2x) + -5x * (3 + 2x)) 9x + 10x2 = 8 + -1(3 + 2x + (3 * -5x + 2x * -5x)) 9x + 10x2 = 8 + -1(3 + 2x + (-15x + -10x2)) Combine like terms: 2x + -15x = -13x 9x + 10x2 = 8 + -1(3 + -13x + -10x2) 9x + 10x2 = 8 + (3 * -1 + -13x * -1 + -10x2 * -1) 9x + 10x2 = 8 + (-3 + 13x + 10x2) Combine like terms: 8 + -3 = 5 9x + 10x2 = 5 + 13x + 10x2 Add '-10x2' to each side of the equation. 9x + 10x2 + -10x2 = 5 + 13x + 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 9x + 0 = 5 + 13x + 10x2 + -10x2 9x = 5 + 13x + 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 9x = 5 + 13x + 0 9x = 5 + 13x Solving 9x = 5 + 13x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13x' to each side of the equation. 9x + -13x = 5 + 13x + -13x Combine like terms: 9x + -13x = -4x -4x = 5 + 13x + -13x Combine like terms: 13x + -13x = 0 -4x = 5 + 0 -4x = 5 Divide each side by '-4'. x = -1.25 Simplifying x = -1.25
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