[tex]\left|\dfrac{4-x}{2x+1}\right|<6\qquad\left(x\not=-\dfrac{1}{2}\right)\\\\\dfrac{4-x}{2x+1}<6 \wedge \dfrac{4-x}{2x+1}>-6\\\\(4-x)(2x+1)<6(2x+1)^2\wedge (4-x)(2x+1)>-6(2x+1)^2\\8x+4-2x^2-x<6(4x^2+4x+1)\wedge8x+4-2x^2-x>-6(4x^2+4x+1)\\8x+4-2x^2-x<24x^2+24x+6\wedge 8x+4-2x^2-x>-24x^2-24x-6\\26x^2+17x+2>0\wedge 22x^2+31x+10>0\\26x^2+13x+4x+2>0\wedge 22x^2+11x+20x+10>0\\13x(2x+1)+2(2x+1)>0\wedge11x(2x+1)+10(2x+1)>0\\(13x+2)(2x+1)>0\wedge (11x+10)(2x+1)>0\\[/tex]
[tex]x\in\left(-\infty,-\dfrac{1}{2}\right)\cup\left(-\dfrac{2}{13},\infty\right) \wedge x\in\left(-\infty,-\dfrac{10}{11}\right)\cup\left(-\dfrac{1}{2},\infty\right)\\\\x\in\left(-\infty,-\dfrac{10}{11}\right)\cup\left(-\dfrac{2}{13},\infty\right)[/tex]
