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Simplifying 3x + -2(2x + 3) = 5 + -1[2x + -3(4 + -1x)] Reorder the terms: 3x + -2(3 + 2x) = 5 + -1[2x + -3(4 + -1x)] 3x + (3 * -2 + 2x * -2) = 5 + -1[2x + -3(4 + -1x)] 3x + (-6 + -4x) = 5 + -1[2x + -3(4 + -1x)] Reorder the terms: -6 + 3x + -4x = 5 + -1[2x + -3(4 + -1x)] Combine like terms: 3x + -4x = -1x -6 + -1x = 5 + -1[2x + -3(4 + -1x)] -6 + -1x = 5 + -1[2x + (4 * -3 + -1x * -3)] -6 + -1x = 5 + -1[2x + (-12 + 3x)] Reorder the terms: -6 + -1x = 5 + -1[-12 + 2x + 3x] Combine like terms: 2x + 3x = 5x -6 + -1x = 5 + -1[-12 + 5x] -6 + -1x = 5 + [-12 * -1 + 5x * -1] -6 + -1x = 5 + [12 + -5x] Combine like terms: 5 + 12 = 17 -6 + -1x = 17 + -5x Solving -6 + -1x = 17 + -5x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5x' to each side of the equation. -6 + -1x + 5x = 17 + -5x + 5x Combine like terms: -1x + 5x = 4x -6 + 4x = 17 + -5x + 5x Combine like terms: -5x + 5x = 0 -6 + 4x = 17 + 0 -6 + 4x = 17 Add '6' to each side of the equation. -6 + 6 + 4x = 17 + 6 Combine like terms: -6 + 6 = 0 0 + 4x = 17 + 6 4x = 17 + 6 Combine like terms: 17 + 6 = 23 4x = 23 Divide each side by '4'. x = 5.75 Simplifying x = 5.75
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