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