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Simplifying 12x + -2(5x + 4) + -3(2x + -1) = 2[x + -2(2x + 1)] Reorder the terms: 12x + -2(4 + 5x) + -3(2x + -1) = 2[x + -2(2x + 1)] 12x + (4 * -2 + 5x * -2) + -3(2x + -1) = 2[x + -2(2x + 1)] 12x + (-8 + -10x) + -3(2x + -1) = 2[x + -2(2x + 1)] Reorder the terms: 12x + -8 + -10x + -3(-1 + 2x) = 2[x + -2(2x + 1)] 12x + -8 + -10x + (-1 * -3 + 2x * -3) = 2[x + -2(2x + 1)] 12x + -8 + -10x + (3 + -6x) = 2[x + -2(2x + 1)] Reorder the terms: -8 + 3 + 12x + -10x + -6x = 2[x + -2(2x + 1)] Combine like terms: -8 + 3 = -5 -5 + 12x + -10x + -6x = 2[x + -2(2x + 1)] Combine like terms: 12x + -10x = 2x -5 + 2x + -6x = 2[x + -2(2x + 1)] Combine like terms: 2x + -6x = -4x -5 + -4x = 2[x + -2(2x + 1)] Reorder the terms: -5 + -4x = 2[x + -2(1 + 2x)] -5 + -4x = 2[x + (1 * -2 + 2x * -2)] -5 + -4x = 2[x + (-2 + -4x)] Reorder the terms: -5 + -4x = 2[-2 + x + -4x] Combine like terms: x + -4x = -3x -5 + -4x = 2[-2 + -3x] -5 + -4x = [-2 * 2 + -3x * 2] -5 + -4x = [-4 + -6x] Solving -5 + -4x = -4 + -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. -5 + -4x + 6x = -4 + -6x + 6x Combine like terms: -4x + 6x = 2x -5 + 2x = -4 + -6x + 6x Combine like terms: -6x + 6x = 0 -5 + 2x = -4 + 0 -5 + 2x = -4 Add '5' to each side of the equation. -5 + 5 + 2x = -4 + 5 Combine like terms: -5 + 5 = 0 0 + 2x = -4 + 5 2x = -4 + 5 Combine like terms: -4 + 5 = 1 2x = 1 Divide each side by '2'. x = 0.5 Simplifying x = 0.5
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