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Simplifying 3(5x + 20) + 5(2x + 3) = 10(4x + -10) + 5(12x + -25) Reorder the terms: 3(20 + 5x) + 5(2x + 3) = 10(4x + -10) + 5(12x + -25) (20 * 3 + 5x * 3) + 5(2x + 3) = 10(4x + -10) + 5(12x + -25) (60 + 15x) + 5(2x + 3) = 10(4x + -10) + 5(12x + -25) Reorder the terms: 60 + 15x + 5(3 + 2x) = 10(4x + -10) + 5(12x + -25) 60 + 15x + (3 * 5 + 2x * 5) = 10(4x + -10) + 5(12x + -25) 60 + 15x + (15 + 10x) = 10(4x + -10) + 5(12x + -25) Reorder the terms: 60 + 15 + 15x + 10x = 10(4x + -10) + 5(12x + -25) Combine like terms: 60 + 15 = 75 75 + 15x + 10x = 10(4x + -10) + 5(12x + -25) Combine like terms: 15x + 10x = 25x 75 + 25x = 10(4x + -10) + 5(12x + -25) Reorder the terms: 75 + 25x = 10(-10 + 4x) + 5(12x + -25) 75 + 25x = (-10 * 10 + 4x * 10) + 5(12x + -25) 75 + 25x = (-100 + 40x) + 5(12x + -25) Reorder the terms: 75 + 25x = -100 + 40x + 5(-25 + 12x) 75 + 25x = -100 + 40x + (-25 * 5 + 12x * 5) 75 + 25x = -100 + 40x + (-125 + 60x) Reorder the terms: 75 + 25x = -100 + -125 + 40x + 60x Combine like terms: -100 + -125 = -225 75 + 25x = -225 + 40x + 60x Combine like terms: 40x + 60x = 100x 75 + 25x = -225 + 100x Solving 75 + 25x = -225 + 100x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-100x' to each side of the equation. 75 + 25x + -100x = -225 + 100x + -100x Combine like terms: 25x + -100x = -75x 75 + -75x = -225 + 100x + -100x Combine like terms: 100x + -100x = 0 75 + -75x = -225 + 0 75 + -75x = -225 Add '-75' to each side of the equation. 75 + -75 + -75x = -225 + -75 Combine like terms: 75 + -75 = 0 0 + -75x = -225 + -75 -75x = -225 + -75 Combine like terms: -225 + -75 = -300 -75x = -300 Divide each side by '-75'. x = 4 Simplifying x = 4
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