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Simplifying 5(3x + -2) + 2(5x + 3) = 7(4x + -1) + -3(5x + -1) Reorder the terms: 5(-2 + 3x) + 2(5x + 3) = 7(4x + -1) + -3(5x + -1) (-2 * 5 + 3x * 5) + 2(5x + 3) = 7(4x + -1) + -3(5x + -1) (-10 + 15x) + 2(5x + 3) = 7(4x + -1) + -3(5x + -1) Reorder the terms: -10 + 15x + 2(3 + 5x) = 7(4x + -1) + -3(5x + -1) -10 + 15x + (3 * 2 + 5x * 2) = 7(4x + -1) + -3(5x + -1) -10 + 15x + (6 + 10x) = 7(4x + -1) + -3(5x + -1) Reorder the terms: -10 + 6 + 15x + 10x = 7(4x + -1) + -3(5x + -1) Combine like terms: -10 + 6 = -4 -4 + 15x + 10x = 7(4x + -1) + -3(5x + -1) Combine like terms: 15x + 10x = 25x -4 + 25x = 7(4x + -1) + -3(5x + -1) Reorder the terms: -4 + 25x = 7(-1 + 4x) + -3(5x + -1) -4 + 25x = (-1 * 7 + 4x * 7) + -3(5x + -1) -4 + 25x = (-7 + 28x) + -3(5x + -1) Reorder the terms: -4 + 25x = -7 + 28x + -3(-1 + 5x) -4 + 25x = -7 + 28x + (-1 * -3 + 5x * -3) -4 + 25x = -7 + 28x + (3 + -15x) Reorder the terms: -4 + 25x = -7 + 3 + 28x + -15x Combine like terms: -7 + 3 = -4 -4 + 25x = -4 + 28x + -15x Combine like terms: 28x + -15x = 13x -4 + 25x = -4 + 13x Add '4' to each side of the equation. -4 + 4 + 25x = -4 + 4 + 13x Combine like terms: -4 + 4 = 0 0 + 25x = -4 + 4 + 13x 25x = -4 + 4 + 13x Combine like terms: -4 + 4 = 0 25x = 0 + 13x 25x = 13x Solving 25x = 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. 25x + -13x = 13x + -13x Combine like terms: 25x + -13x = 12x 12x = 13x + -13x Combine like terms: 13x + -13x = 0 12x = 0 Divide each side by '12'. x = 0 Simplifying x = 0
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