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

1 answer:

5 0

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

or:

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

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