| x + 16 2 x − 3 | > 3 {\displaystyle {\begin{aligned}\left|{\frac {x+16}{2x-3}}\right\vert >3\end{aligned}}} x + 16 2 x − 3 > 3 {\displaystyle {\frac {x+16}{2x-3}}>3} או X + 16 2 X − 3 < − 3 {\displaystyle {\frac {X+16}{2X-3}}<-3} כאשר X ≠ 1.5 {\displaystyle X\neq 1.5}
X + 16 2 X − 3 < − 3 X + 16 2 X − 3 + 3 < 0 x + 16 + 3 ( 2 x − 3 ) 2 x − 3 < 0 x + 16 + 6 x − 9 2 x − 3 < 0 7 x + 7 2 x − 3 < 0 / + ( 2 x − 3 ) 2 ( 7 x + 7 ) ( 2 x − 3 ) < 0 ( 7 x + 7 ) ( 2 x − 3 ) = 0 x 1 = − 1 x 2 = 1.5 ↓ − 14 < x < 1.5 {\displaystyle {\begin{aligned}&{\frac {X+16}{2X-3}}<-3\\&{\frac {X+16}{2X-3}}+3<0\\&{\frac {x+16+3(2x-3)}{2x-3}}<0\\&{\frac {x+16+6x-9}{2x-3}}<0\\&{\frac {7x+7}{2x-3}}<0/+(2x-3)^{2}\\&(7x+7)(2x-3)<0\\&(7x+7)(2x-3)=0\\&x_{1}=-1&x_{2}=1.5\\&\downarrow \\&-14<x<1.5\\\end{aligned}}}
− 1 < x < 5 x ≠ 1.5 {\displaystyle {\begin{aligned}-1<x<5&x\neq 1.5\end{aligned}}}
