Question

giải bất pt

a)\(\dfrac{1-2x}{4}-1< \dfrac{1-6x}{8}\)

b)\(\dfrac{x-1}{3}-2x>\dfrac{3x+1}{2}\)

Answer 1

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

 

Answer 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)\(\dfrac{x-1}{3}-2x>\dfrac{3x+1}{2}\)

\(\Leftrightarrow\dfrac{x-1-6x}{3}>\dfrac{3x+1}{2}\)

\(\Leftrightarrow2\left(-5x-1\right)>3\left(3x+1\right)\)

\(\Leftrightarrow-10x-2>9x+3\)

\(\Leftrightarrow-19x>5\)

\(\Leftrightarrow x< \dfrac{-5}{19}\)