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Simplifying 2(3x + -4) + 3(2x + -5) = 5(2x + -7) + 8 Reorder the terms: 2(-4 + 3x) + 3(2x + -5) = 5(2x + -7) + 8 (-4 * 2 + 3x * 2) + 3(2x + -5) = 5(2x + -7) + 8 (-8 + 6x) + 3(2x + -5) = 5(2x + -7) + 8 Reorder the terms: -8 + 6x + 3(-5 + 2x) = 5(2x + -7) + 8 -8 + 6x + (-5 * 3 + 2x * 3) = 5(2x + -7) + 8 -8 + 6x + (-15 + 6x) = 5(2x + -7) + 8 Reorder the terms: -8 + -15 + 6x + 6x = 5(2x + -7) + 8 Combine like terms: -8 + -15 = -23 -23 + 6x + 6x = 5(2x + -7) + 8 Combine like terms: 6x + 6x = 12x -23 + 12x = 5(2x + -7) + 8 Reorder the terms: -23 + 12x = 5(-7 + 2x) + 8 -23 + 12x = (-7 * 5 + 2x * 5) + 8 -23 + 12x = (-35 + 10x) + 8 Reorder the terms: -23 + 12x = -35 + 8 + 10x Combine like terms: -35 + 8 = -27 -23 + 12x = -27 + 10x Solving -23 + 12x = -27 + 10x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10x' to each side of the equation. -23 + 12x + -10x = -27 + 10x + -10x Combine like terms: 12x + -10x = 2x -23 + 2x = -27 + 10x + -10x Combine like terms: 10x + -10x = 0 -23 + 2x = -27 + 0 -23 + 2x = -27 Add '23' to each side of the equation. -23 + 23 + 2x = -27 + 23 Combine like terms: -23 + 23 = 0 0 + 2x = -27 + 23 2x = -27 + 23 Combine like terms: -27 + 23 = -4 2x = -4 Divide each side by '2'. x = -2 Simplifying x = -2
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