Question

Solve the absolute value inequality 5|3-2x|+1<4

Answer 1

`5\cdot|3-2x|+1\ \textless \ 4\qquad|-1\\\\5\cdot|3-2x|+1-1\ \textless \ 4-1\\\\5\cdot|3-2x|\ \textless \ 3\qquad|:5\\\\|3-2x|\ \textless \ (3)/(5)\\\\\\\\-(3)/(5)\ \textless \ 3-2x\ \textless \ (3)/(5)\qquad\Big|-3\\\\\\ -(3)/(5)-3\ \textless \ 3-2x-3\ \textless \ (3)/(5)-3\\\\\\-(18)/(5)\ \textless \ -2x\ \textless \ -(12)/(5)\qquad\Big|:(-2)\\\\\\(9)/(5)\ \textgreater \ x\ \textgreater \ (6)/(5)\\\\\\\boxed{x\in\left((6)/(5);(9)/(5)\right)}`

or:


`\boxed{x\in\left(1.2;1.8\right)}`