Tìm x, biết:
1$\frac{1}{30}$ : ( 24$\frac{1}{6}$ – 24$\frac{1}{5}$ ) – $\frac{1\frac{1}{2}-\frac{3}{4}}{4x-\frac{1}{2}}$ = ( -1$\frac{1}{15}$ ) : ( 8$\frac{1}{5}$ – 8$\frac{1}{3}$)
Tìm x, biết:
1$\frac{1}{30}$ : ( 24$\frac{1}{6}$ – 24$\frac{1}{5}$ ) – $\frac{1\frac{1}{2}-\frac{3}{4}}{4x-\frac{1}{2}}$ = ( -1$\frac{1}{15}$ ) : ( 8$\frac{1}{5}$ – 8$\frac{1}{3}$)
`1 1/30:(24 1/6-24 1/5)-( 1 1/2-3/4)/(4x-1/2)=(-1 1/15):(8 1/5-8 1/3)`
`=>31/30:(145/6-121/5)-(3/2-3/4)/(4x-1/2)=(-15)/16:(1/5-1/3)`
`=>31/30:(-1)/30-3/(4(4x-1/2))=(-15)/16:(-2)/15`
`=>(-31)-3/(4(4x-1/2))=8`
`=>(-31)-3/(16x-2)=8`
`=>3/(16x-2)=(-31)-8`
`=>3/(16x-2)=(-39)`
`=>16x-2=-1/13`
`=>16x=-1/13+2`
`=>16x=(-25)/13`
`=>x=(-25)/13:16`
`=>x=(-25)/208`
Vậy `x=(-25)/208`
Đáp án:
$\frac{25}{108}$
Giải thích các bước giải:
1$\frac{1}{30}$ : ( 24$\frac{1}{6}$ – 24$\frac{1}{5}$ ) – $\frac{1\frac{1}{2}-\frac{3}{4}}{4x-\frac{1}{2}}$ = ( -1$\frac{1}{15}$ ) : ( 8$\frac{1}{5}$ – 8$\frac{1}{3}$) (1)
Ta có:
1$\frac{1}{30}$ : ( 24$\frac{1}{6}$ – 24$\frac{1}{5}$ )
= $\frac{31}{30}$ : ( $\frac{145}{6}$ – $\frac{121}{5}$ )
= $\frac{31}{30}$ : $\frac{-1}{30}$
1$\frac{1}{2}$-$\frac{3}{4}$
= $\frac{3}{2}$ – $\frac{3}{4}$
= $\frac{6-3}{4}$
= $\frac{3}{4}$
= -31
( -1$\frac{1}{15}$ ) : ( 8$\frac{1}{5}$ – 8$\frac{1}{3}$)
= $\frac{-16}{15}$ : ($\frac{1}{5}$ – $\frac{1}{3}$ )
= $\frac{-16}{15}$ : $\frac{-2}{15}$
= 8
Suy ra:
(1) ⇔ -31 – $\frac{3}{4(4x -\frac{1}{2})}$ = 8
⇔ -31 – $\frac{3}{16x -2}$ = 8
⇔ $\frac{3}{16x -2}$ = -39
⇔ 16x – 2 = $\frac{3}{-39}$ = -$\frac{1}{13}$
⇔ 16x = 2 – $\frac{1}{13}$ = $\frac{26-1}{13}$ = $\frac{25}{13}$
⇔ x = $\frac{25}{13×16}$ = $\frac{25}{108}$