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Simplifying 7(2x + 3) + -3(5x + -2) = 5(3x + -4) + -3(3x + -4) Reorder the terms: 7(3 + 2x) + -3(5x + -2) = 5(3x + -4) + -3(3x + -4) (3 * 7 + 2x * 7) + -3(5x + -2) = 5(3x + -4) + -3(3x + -4) (21 + 14x) + -3(5x + -2) = 5(3x + -4) + -3(3x + -4) Reorder the terms: 21 + 14x + -3(-2 + 5x) = 5(3x + -4) + -3(3x + -4) 21 + 14x + (-2 * -3 + 5x * -3) = 5(3x + -4) + -3(3x + -4) 21 + 14x + (6 + -15x) = 5(3x + -4) + -3(3x + -4) Reorder the terms: 21 + 6 + 14x + -15x = 5(3x + -4) + -3(3x + -4) Combine like terms: 21 + 6 = 27 27 + 14x + -15x = 5(3x + -4) + -3(3x + -4) Combine like terms: 14x + -15x = -1x 27 + -1x = 5(3x + -4) + -3(3x + -4) Reorder the terms: 27 + -1x = 5(-4 + 3x) + -3(3x + -4) 27 + -1x = (-4 * 5 + 3x * 5) + -3(3x + -4) 27 + -1x = (-20 + 15x) + -3(3x + -4) Reorder the terms: 27 + -1x = -20 + 15x + -3(-4 + 3x) 27 + -1x = -20 + 15x + (-4 * -3 + 3x * -3) 27 + -1x = -20 + 15x + (12 + -9x) Reorder the terms: 27 + -1x = -20 + 12 + 15x + -9x Combine like terms: -20 + 12 = -8 27 + -1x = -8 + 15x + -9x Combine like terms: 15x + -9x = 6x 27 + -1x = -8 + 6x Solving 27 + -1x = -8 + 6x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6x' to each side of the equation. 27 + -1x + -6x = -8 + 6x + -6x Combine like terms: -1x + -6x = -7x 27 + -7x = -8 + 6x + -6x Combine like terms: 6x + -6x = 0 27 + -7x = -8 + 0 27 + -7x = -8 Add '-27' to each side of the equation. 27 + -27 + -7x = -8 + -27 Combine like terms: 27 + -27 = 0 0 + -7x = -8 + -27 -7x = -8 + -27 Combine like terms: -8 + -27 = -35 -7x = -35 Divide each side by '-7'. x = 5 Simplifying x = 5
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