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Simplifying 8x + 7(15 + -6x) = 75 + x + 30(5 + -3x) 8x + (15 * 7 + -6x * 7) = 75 + x + 30(5 + -3x) 8x + (105 + -42x) = 75 + x + 30(5 + -3x) Reorder the terms: 105 + 8x + -42x = 75 + x + 30(5 + -3x) Combine like terms: 8x + -42x = -34x 105 + -34x = 75 + x + 30(5 + -3x) 105 + -34x = 75 + x + (5 * 30 + -3x * 30) 105 + -34x = 75 + x + (150 + -90x) Reorder the terms: 105 + -34x = 75 + 150 + x + -90x Combine like terms: 75 + 150 = 225 105 + -34x = 225 + x + -90x Combine like terms: x + -90x = -89x 105 + -34x = 225 + -89x Solving 105 + -34x = 225 + -89x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '89x' to each side of the equation. 105 + -34x + 89x = 225 + -89x + 89x Combine like terms: -34x + 89x = 55x 105 + 55x = 225 + -89x + 89x Combine like terms: -89x + 89x = 0 105 + 55x = 225 + 0 105 + 55x = 225 Add '-105' to each side of the equation. 105 + -105 + 55x = 225 + -105 Combine like terms: 105 + -105 = 0 0 + 55x = 225 + -105 55x = 225 + -105 Combine like terms: 225 + -105 = 120 55x = 120 Divide each side by '55'. x = 2.181818182 Simplifying x = 2.181818182
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