Question

Giải các bất phương trình sau:

a) \(\dfrac{5x-17}{14}+\dfrac{x-3}{26}>\dfrac{29-9x}{91}\)

b)\(\dfrac{8x-1}{9}+\dfrac{3x-2}{4}< \dfrac{43+8x}{12}+\dfrac{35x}{36}\)

c)\(\dfrac{x-2}{5}+\dfrac{2\left(x+1\right)}{3}>\dfrac{13x-8}{15}\)

Answer 1

a.

\(\dfrac{5x-17}{14}+\dfrac{x-3}{26}>\dfrac{29-9x}{91}\)

\(\Leftrightarrow13\left(5x-17\right)+7\left(x-3\right)>2\left(29-9x\right)\)

\(\Leftrightarrow65x-221+7x-21>58-18x\)

\(\Leftrightarrow65x+7x+18x>58+21+221\)

\(\Leftrightarrow90x>300\)

\(\Leftrightarrow x>\dfrac{10}{3}\)

Answer 2

b)

\(\dfrac{8x-1}{9}+\dfrac{3x-2}{4}< \dfrac{43+8x}{12}+\dfrac{35x}{36}\)

\(\Leftrightarrow4\left(8x-1\right)+9\left(3x-2\right)< 3\left(43+8x\right)+35x\)

\(\Leftrightarrow32x-4+27x-18< 129+24x+35x\)

\(\Leftrightarrow32x+27x-24x-35x< 129+18+4\)

\(\Leftrightarrow0x< 151\) ( luôn đúng)

Vậy bất pt vô số nghiệm

Answer 3

c) \(\dfrac{x-2}{5}+\dfrac{2\left(x+1\right)}{3}>\dfrac{13x-8}{15}\)

\(\Leftrightarrow\dfrac{3x-6}{15}+\dfrac{10x+10}{15}>\dfrac{13x-8}{15}\)

\(\Rightarrow\)3x+10x-6+10>13x-8

\(\Leftrightarrow\)13x-13x+8+4>0

\(\Leftrightarrow0x+12>0\) (vô nghiệm)