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Simplifying x + 6(x + -2) + -3(x + -1) = 5(x + 1) + 2x Reorder the terms: x + 6(-2 + x) + -3(x + -1) = 5(x + 1) + 2x x + (-2 * 6 + x * 6) + -3(x + -1) = 5(x + 1) + 2x x + (-12 + 6x) + -3(x + -1) = 5(x + 1) + 2x Reorder the terms: x + -12 + 6x + -3(-1 + x) = 5(x + 1) + 2x x + -12 + 6x + (-1 * -3 + x * -3) = 5(x + 1) + 2x x + -12 + 6x + (3 + -3x) = 5(x + 1) + 2x Reorder the terms: -12 + 3 + x + 6x + -3x = 5(x + 1) + 2x Combine like terms: -12 + 3 = -9 -9 + x + 6x + -3x = 5(x + 1) + 2x Combine like terms: x + 6x = 7x -9 + 7x + -3x = 5(x + 1) + 2x Combine like terms: 7x + -3x = 4x -9 + 4x = 5(x + 1) + 2x Reorder the terms: -9 + 4x = 5(1 + x) + 2x -9 + 4x = (1 * 5 + x * 5) + 2x -9 + 4x = (5 + 5x) + 2x Combine like terms: 5x + 2x = 7x -9 + 4x = 5 + 7x Solving -9 + 4x = 5 + 7x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7x' to each side of the equation. -9 + 4x + -7x = 5 + 7x + -7x Combine like terms: 4x + -7x = -3x -9 + -3x = 5 + 7x + -7x Combine like terms: 7x + -7x = 0 -9 + -3x = 5 + 0 -9 + -3x = 5 Add '9' to each side of the equation. -9 + 9 + -3x = 5 + 9 Combine like terms: -9 + 9 = 0 0 + -3x = 5 + 9 -3x = 5 + 9 Combine like terms: 5 + 9 = 14 -3x = 14 Divide each side by '-3'. x = -4.666666667 Simplifying x = -4.666666667
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