Giải phương trình 3/4 + 1/4:x - 1/2 = 2/3 (2025)

#Toán lớp 6

1

\(\dfrac{3}{4}+\dfrac{1}{4}:x-\dfrac{1}{2}=\dfrac{2}{3}\\\dfrac{3}{4}+\dfrac{1}{4}:x=\dfrac{2}{3}+\dfrac{1}{2}=\dfrac{7}{6}\\\dfrac{1}{4}:x=\dfrac{7}{6}-\dfrac{3}{4}\\\dfrac{1}{4}:x=\dfrac{5}{12}\\x=\dfrac{1}{4}:\dfrac{5}{12}\\x=\dfrac{1}{4}\cdot\dfrac{12}{5}=\dfrac{3}{5}\)

TP

a: =>x-2/5=3/4:1/3=3/4*3=9/4

=>x=9/4+2/5=45/20+8/20=53/20

b: =>x-2/3=7/3:4/5=7/3*5/4=35/12

=>x=35/12+2/3=43/12

c: 1/3(x-2/5)=4/5

=>x-2/5=4/5*3=12/5

=>x=12/5+2/5=14/5

d: =>2/3x-1/3-1/4x+1/10=7/3

=>5/12x-7/30=7/3

=>5/12x=7/3+7/30=77/30

=>x=77/30:5/12=154/25

e:\(\Leftrightarrow x\cdot\dfrac{3}{7}-\dfrac{2}{7}+\dfrac{1}{2}-\dfrac{5}{4}x+\dfrac{5}{2}=0\)

=>\(x\cdot\dfrac{-23}{28}=\dfrac{2}{7}-3=\dfrac{-19}{7}\)

=>x=19/7:23/28=76/23

f: =>1/2x-3/2+1/3x-4/3+1/4x-5/4=1/5

=>13/12x=1/5+3/2+4/3+5/4=257/60

=>x=257/65

i: =>x^2-2/5x-x^2-2x+11/4=4/3

=>-12/5x=4/3-11/4=-17/12

=>x=17/12:12/5=85/144

HP

a)\(x-\dfrac{3}{4}=6\times\dfrac{3}{8}\)

\(x-\dfrac{3}{4}=\dfrac{9}{4}\)

=>\(x=\dfrac{9}{4}+\dfrac{3}{4}=3\)

b)\(\dfrac{7}{8}:x=3-\dfrac{1}{2}\)

\(\dfrac{7}{8}:x=\dfrac{5}{2}\)

=>\(x=\dfrac{7}{8}:\dfrac{5}{2}=\dfrac{7}{20}\)

c)\(x+\dfrac{1}{2}\times\dfrac{1}{3}=\dfrac{3}{4}\)

\(x+\dfrac{1}{6}=\dfrac{3}{4}\)

=>\(x=\dfrac{3}{4}-\dfrac{1}{6}=\dfrac{7}{12}\)

d)\(\dfrac{3}{2}\times\dfrac{4}{5}-x=\dfrac{2}{3}\)

\(\dfrac{6}{5}-x=\dfrac{2}{3}\)

=>\(x=\dfrac{6}{5}-\dfrac{2}{3}=\dfrac{8}{15}\)

e)\(x\times3\dfrac{1}{3}=3\dfrac{1}{3}:4\dfrac{1}{4}\)(?)

\(x\times\dfrac{10}{3}=\dfrac{40}{51}\)

=>\(x=\dfrac{40}{51}:\dfrac{10}{3}=\dfrac{4}{17}\)

f)\(5\dfrac{2}{3}:x=3\dfrac{2}{3}-2\)

\(\dfrac{17}{3}:x=\dfrac{5}{3}\)

=>\(x=\dfrac{17}{3}:\dfrac{5}{3}=\dfrac{17}{5}\)

a: =>x-3/4=18/8=9/4

=>x=9/4+3/4=12/4=3

b: =>7/8:x=5/2

=>x=7/8:5/2=7/8*2/5=14/40=7/20

c: x+1/2*1/3=3/4

=>x+1/6=3/4

=>x=3/4-1/6=9/12-2/12=7/12

d: =>12/10-x=2/3

=>6/5-x=2/3

=>x=6/5-2/3=18/15-10/15=8/15

e: =>x*10/3=10/3:17/4=10/3*4/17

=>x=4/17

f: =>17/3:x=13/3-5/2=26/6-15/6=11/6

=>x=17/3:11/6=17/3*6/11=34/11

NV

a) 3 3/4 . x = 1 1/2

<=> 15/4 . x = 3/2

<=> x = 3/4 . 4/15

<=> x = 1/5

Vậy x = 1/5

b) 1 1/4 x + 1 1/2 = 1 1/4

<=> 5/4 . x + 3/2 = 5/4

<=> 5/4 . x = 5/4 - 3/2

<=> 5/4 . x = -1/4

<=> x = -1/4 . 4/5

<=> x = -1/5

Vậy x = -1/5

c) ( 3 1/3 - 1 1/2 x ) : 5/6 = 1 1/2

<=> ( 10/3 - 3/2 x ) : 5/6 = 3/2

<=> 10/3 - 3/2 x = 3/2 . 5/6

<=> 10/3 - 3/2 x = 5/4

<=> 3/2 . x = 10/3 - 5/4

<=> 3/2 . x = 25/12

<=> x = 25/12 . 2/3

<=> x = 25/18

Vậy x = 25/18

d) ( 3/7 x - 1 ) : 4 = -1/28

<=> 3/7 . x - 1 = -1/28 . 1/4

<=> 3/7 . x - 1 = -1/112

<=> 3/7 . x = -1/112 + 1

<=> 3/7 . x = 111/112

<=> x = 111/112 . 7/3

<=> x = 37/16

Vậy x = 37/16

e) | x - 3/4 | = 1

<=> x - 3/4 = 1

hoặc x - 3/4 = -1

<=> x = 1 + 3/4

hoặc x = -1 + 3/4

<=> x = 7/4

hoặc x = -1/4

Vậy x = 7/4 ; x = -1/4

f) | 2/3 . x + 1/3 | = 5/6

<=> 2/3 . x + 1/3 = 5/6

hoặc 2/3 . x + 1/3 = -5/6

<=> 2/3 . x = 5/6 - 1/3

hoặc 2/3 . x = -5/6 - 1/3

<=> 2/3 . x = 1/2

hoặc 2/3 . x = -7/6

<=> x = 1/2 . 3/2

hoặc x = -7/6 . 3/2

<=> x = 3/4

hoặc x = -7/4

Vậy x = 3/4 ; x = -7/4

LK

HP

`x + 2 3/4 = 5 2/3`

`=> x + 11/4 = 17/3`

`=> x= 17/3 -11/4`

`=>x=35/12`

__

`x - 1 4/5 = 3 2/7`

`=> x- 9/5 = 23/7`

`=> x= 23/7 +9/5`

`=>x=178/35`

__

`x xx 3 1/2 =4 3/4`

`=> x xx7/2 =19/4`

`=> x= 19/4: 7/2`

`=> x= 19/4 xx 2/7`

`=> x= 19/14`

__

`x : 2 2/3 = 4 1/3`

`=> x : 8/3 = 13/3`

`=> x= 13/3 xx 8/3`

`=>x=104/9`

a: =>x+11/4=17/3

=>x=17/3-11/4=68/12-33/12=35/12

b: =>x-9/5=23/7

=>x=23/7+9/5=178/35

c: =>x*7/2=4,75

=>x=19/4:7/2=19/14

d: =>x:8/3=13/3

=>x=13/3*8/3=104/9

H

1) 1/3 . x + (2/3 - 4/9) = -3/4

1/3 . x + 2/9 = -3/4

1/3 . x = -3/4 - 2/9

1/3 . x = -35/36

x = -35/36 : 1/3

x = -35/12

LT

PA

+)\(\dfrac{1}{3}x=-\dfrac{4}{3}-\dfrac{1}{2}=-\dfrac{11}{6}\)

\(x=-\dfrac{11}{6}:\dfrac{1}{3}=-\dfrac{11}{2}\)

+)\(\dfrac{4}{3}x=-\dfrac{2}{3}+\dfrac{1}{2}=-\dfrac{1}{6}\)

\(x=-\dfrac{1}{6}:\dfrac{4}{3}=-\dfrac{1}{8}\)

+)\(2\left(x-1\right)=\dfrac{5}{2}+\dfrac{2}{3}=\dfrac{19}{6}\)

\(x-1=\dfrac{19}{12}\)

\(x=\dfrac{31}{12}\)

\(\dfrac{1}{3}x+\dfrac{1}{2}=-\dfrac{4}{3}\)

\(\dfrac{1}{3}x=\left(-\dfrac{4}{3}\right)-\dfrac{1}{2}\)

\(\dfrac{1}{3}x=-\dfrac{11}{6}\)

\(x=\left(-\dfrac{11}{6}\right):\dfrac{1}{3}\)

\(x=-\dfrac{11}{2}\)

\(-\dfrac{2}{3}-\dfrac{4}{3}x=-\dfrac{1}{2}\)

\(\dfrac{4}{3}x=\left(-\dfrac{2}{3}\right)-\dfrac{-1}{2}\)

\(\dfrac{4}{3}x=-\dfrac{1}{6}\)

\(x=\left(-\dfrac{1}{6}\right):\dfrac{4}{3}\)

\(x=-\dfrac{1}{8}\)

\(\dfrac{5}{2}-2\left(x-1\right)=-\dfrac{2}{3}\)

\(2\left(x-1\right)=\dfrac{5}{2}-\left(-\dfrac{2}{3}\right)\)

\(2\left(x-1\right)=\dfrac{19}{6}\)

\(\left(x-1\right)=\dfrac{19}{6}:2\)

\(x-1=\dfrac{19}{12}\)

\(x=\dfrac{19}{12}+1\)

\(x=\dfrac{31}{12}\)

DT

`@` ` \text {Ans}`

`\downarrow`

`a,`

`1/4+3/4*x=3/2-x`

`=> 1/4 + 3/4x - 3/2 + x = 0`

`=> (1/4 - 3/2) + (3/4x + x) = 0`

`=> -5/4 + 7/4x = 0`

`=> 7/4x = 5/4`

`=> x = 5/4 \div 7/4`

`=> x = 5/7`

Vậy, `x=5/7`

`b,`

`3/5*x-1/4=1/10*x-1/2`

`=> 3/5x - 1/4 - 1/10x + 1/2 = 0`

`=> (3/5x - 1/10x) + (-1/4 + 1/2)=0`

`=> 1/2x + 1/4 = 0`

`=> 1/2x = -1/4`

`=> x = -1/4 \div 1/2`

`=> x = -1/2`

Vậy, `x=-1/2`

`c,`

`3x-3/5=x-1/4`

`=> 3x - 3/5 - x + 1/4 = 0`

`=> (3x - x) - (3/5 - 1/4) = 0`

`=> 2x - 7/20 = 0`

`=> 2x = 0,35`

`=> x = 0,35 \div 2`

`=> x = 7/40`

Vậy, `x=7/40`

`d,`

`3/2*x-2/5=1/3*x-1/4`

`=> 3/2x - 2/5 - 1/3x + 1/4 = 0`

`=> (3/2x - 1/3x) - (2/5 - 1/4) = 0`

`=> 7/6x - 3/20 = 0`

`=> 7/6x = 3/20`

`=> x = 3/20 \div 7/6`

`=> x = 9/70`

Vậy, `x=9/70`

`@` `\text {Kaizuu lv uuu}`

D