A 1-2x/4-1<1-6x/8
<=>2(1-2x)-8<1-6x
<=>2-4x-8<1-6x
<=>-4x+6x<1-2+8
<=>2x<7
<=>x<7/2
a)\(\dfrac{1-2x}{4}-1< \dfrac{1-6x}{8}\)
\(\Leftrightarrow\dfrac{1-2x-4}{4}< \dfrac{1-6x}{8}\)
\(\Leftrightarrow8\left(-3-2x\right)< 4\left(1-6x\right)\)
\(\Leftrightarrow-24+16x< 4-24x\)
\(\Leftrightarrow40x< 28\)
\(\Leftrightarrow x< \dfrac{7}{10}\)
b)\(\dfrac{x-1}{3}-2x>\dfrac{3x+1}{2}\)
\(\Leftrightarrow\dfrac{x-1-6x}{3}>\dfrac{3x+1}{2}\)
\(\Leftrightarrow2\left(-5x-1\right)>3\left(3x+1\right)\)
\(\Leftrightarrow-10x-2>9x+3\)
\(\Leftrightarrow-19x>5\)
\(\Leftrightarrow x< \dfrac{-5}{19}\)
