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Simplifying 6(x + -7) + -7(x + -6) = x + 6 + -1(-1x + -5) Reorder the terms: 6(-7 + x) + -7(x + -6) = x + 6 + -1(-1x + -5) (-7 * 6 + x * 6) + -7(x + -6) = x + 6 + -1(-1x + -5) (-42 + 6x) + -7(x + -6) = x + 6 + -1(-1x + -5) Reorder the terms: -42 + 6x + -7(-6 + x) = x + 6 + -1(-1x + -5) -42 + 6x + (-6 * -7 + x * -7) = x + 6 + -1(-1x + -5) -42 + 6x + (42 + -7x) = x + 6 + -1(-1x + -5) Reorder the terms: -42 + 42 + 6x + -7x = x + 6 + -1(-1x + -5) Combine like terms: -42 + 42 = 0 0 + 6x + -7x = x + 6 + -1(-1x + -5) 6x + -7x = x + 6 + -1(-1x + -5) Combine like terms: 6x + -7x = -1x -1x = x + 6 + -1(-1x + -5) Reorder the terms: -1x = x + 6 + -1(-5 + -1x) -1x = x + 6 + (-5 * -1 + -1x * -1) -1x = x + 6 + (5 + 1x) Reorder the terms: -1x = 6 + 5 + x + 1x Combine like terms: 6 + 5 = 11 -1x = 11 + x + 1x Combine like terms: x + 1x = 2x -1x = 11 + 2x Solving -1x = 11 + 2x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2x' to each side of the equation. -1x + -2x = 11 + 2x + -2x Combine like terms: -1x + -2x = -3x -3x = 11 + 2x + -2x Combine like terms: 2x + -2x = 0 -3x = 11 + 0 -3x = 11 Divide each side by '-3'. x = -3.666666667 Simplifying x = -3.666666667
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