Ôn tập chương III

Giải:

a) \(\dfrac{2}{3}x-\dfrac{1}{5}x=-\dfrac{7}{30}\)

\(\Leftrightarrow x\left(\dfrac{2}{3}-\dfrac{1}{5}\right)=-\dfrac{7}{30}\)

\(\Leftrightarrow\dfrac{7}{15}x=-\dfrac{7}{30}\)

\(\Leftrightarrow x=-\dfrac{7}{30}:\dfrac{7}{15}\)

\(\Leftrightarrow x=-\dfrac{1}{2}\)

Vậy ...

b) \(-\dfrac{5}{23}.\dfrac{23}{5}< x< -\dfrac{13}{17}.\dfrac{34}{13}\)

\(\Leftrightarrow-1< x< -2\)

\(\Leftrightarrow x\in\varnothing\)

Vậy ...

a)\(\dfrac{2}{3}\)x - \(\dfrac{1}{5}\)x = \(\dfrac{-7}{30}\)

x\(\left(\dfrac{2}{3}-\dfrac{1}{5}\right)\)= \(\dfrac{-7}{30}\)

x. \(\dfrac{7}{15}\)=\(\dfrac{-7}{30}\)

x = \(\dfrac{-7}{30}\): \(\dfrac{7}{15}\)= \(\dfrac{-7}{30}\). \(\dfrac{15}{7}\)= \(\dfrac{-1}{2}\)

mk chỉ bt làm câu a thôi ak

mong bn thông cảm

b) \(\dfrac{-5}{23}.\dfrac{23}{5}< x< \dfrac{-13}{17}.\dfrac{34}{13}\)

\(\Rightarrow-1< x< -2\)

\(\Rightarrow\) không có giá trị nào của x

Để A lớn nhất thì x-96=1

hay x=97

Để A nhỏ nhất thì x-96=-1

=>x=95

Ta có:

A=\(\dfrac{2n+5}{3n+1}\)=\(\dfrac{2.\left[3n+1\right]+3}{3n+1}\)=\(\dfrac{2.\left[3n+1\right]}{3n+1}\)+\(\dfrac{3}{3n+1}\)= 2+\(\dfrac{3}{3n+1}\)

De A=\(\dfrac{2n+5}{3n+1}\) là số nguyên thì 2+\(\dfrac{3}{3n+1}\)là số nguyên

Suy ra:\(\dfrac{3}{3n+1}\)là số nguyên

Suy ra:3 chia hết cho 3n+1

Suy ra 3n+1 thuộc Ư[3]

Mà Ư[3]={1;-1;3;-3}

Suy ra:3n+1 thuộc {1;-1;3;-3}

+]3n+1=1

3n=1-1

3n=0

n=0:3

n=0[thỏa mãn]

+]3n+1=-1

3n=-1-1

3n=-2

n=-2:3

n=\(\dfrac{-2}{3}\)[loại]

+]3n+1=3

3n=3-1

3n=2

n=2:3

n=\(\dfrac{2}{3}\)[loại]

+]3n+1=-3

3n=-3-1

3n=-4

n=-4:3

n=\(\dfrac{-4}{3}\)[loại]

vậy giá trị cần n tìm là:0

Mình cũng không chắc lắm,nếu có chỗ nào sai mong bạn thứ lỗi.

Để A có giá trị nguyên ⇔ 2n+5 ⋮ 3n+1

⇔ 3(2n+5) - 2(3n+1) ⋮ 3n+1

⇔ 6n + 15 - 6n - 2 ⋮ 3n+1

⇔ 13 ⋮ 3n+1

⇒ 3n+1 ∈ Ư(13) = { 1 ; -1 ; 13; -13 }

ta có bảng

Vậy n ∈ { 0 ; 4 } để A có giá trị nguyên

Bài 2.

A = -3/5 + ( -2/5 + 2 )

A = -3/5 + ( -2/5 + 10/5 )

A = -3/5 + 8/5

A = 5/5

A = 1

--------------------------------------------------------

B = 3/7 + ( -1/5 + -3/7 )

B = 3/7 + ( -7/35 + -15/35 )

B = 3/7 + ( -22/35 )

B = 15/35 + ( -22/35 )

B = -1/5

-----------------------------------------------------

C = ( -5/24 + 0,75 + 7/12 ) : ( -2 . 1/8 )

C = ( -5/24 + 3/4 + 7/12 ) : ( -1/4 )

C = 9/8 : ( -1/4 )

C = 9/8 . ( -4 )

C = -9/2

Bài 3 .

a) 4/7 - x = 1/2 . x + 2/7

<=> -x - x = 1/2 - 4/7 + 2/7

<=> -2x = 3/14

<=> x = 3/14 . ( -1/2 )

<=> x = -3/28

Vậy x = -3/28

b) x : 3 1/5 = 1 1/2

<=> x : 16/5 = 3/2

<=> x = 3/2 . 16/5

<=> x = 24/5

Vậy x = 24/5

c) x . 3/4 = -1 5/8

<=> x . 3/4 = -13/8

<=> x = -13/8 . 4/3

<=> x = -13/6

Vậy x = -13/6

Bài 4.

a) ( 2 1/3 + 3 1/2 ) . x = -4 1/6 + 3 1/7

<=> ( 7/3 + 7/2 ) . x = -25/6 + 22/7

<=> 35/6 . x = -43/42

<=> x = -43/42 . 6/35

<=> x = -43/245

Vậy x = -43/245

b) x : ( 3 1/2 - 5 1/6 ) = 4 1/5 - 6 2/3

<=> x : ( 7/2 - 31/6 ) = 21/5 - 20/3

<=> x : ( 21/6 - 31/6 ) = -37/15

<=> x : ( -5/3 ) = -37/15

<=> x = -37/15 . ( -5/3 )

<=> x = 37/9

Vậy x = 37/9

\(\dfrac{2}{3}x-\dfrac{1}{2}x=\dfrac{5}{12}\)

\(\Rightarrow x\left(\dfrac{2}{3}-\dfrac{1}{2}\right)=\dfrac{5}{12}\)

\(\Rightarrow x.\dfrac{1}{6}=\dfrac{5}{12}\)

\(\Rightarrow x=\dfrac{5}{2}\)

\(\dfrac{2}{3}x-\dfrac{1}{2}x=\dfrac{5}{12}\)

\(\Rightarrow\left(\dfrac{2}{3}-\dfrac{1}{2}\right)x=\dfrac{5}{12}\)

\(\Rightarrow\dfrac{1}{6}x=\dfrac{5}{12}\)

\(\Rightarrow x=\dfrac{5}{2}\)

Vậy \(x=\dfrac{5}{2}\)

Ta có:

\(\dfrac{2}{3}x-\dfrac{1}{2}x=\dfrac{5}{12}\)

\(\Rightarrow x\left(\dfrac{2}{3}-\dfrac{1}{2}\right)=\dfrac{5}{12}\)

\(\Rightarrow\dfrac{1}{6}x=\dfrac{5}{12}\)

\(\Rightarrow x=\dfrac{5}{2}\)

Vậy: \(x=\dfrac{5}{2}\)

chúc bạn học giỏi và đạt thành tích cao!!

a) \(1\dfrac{13}{15}.\left(-5\right)^2.3+\left(\dfrac{8}{15}-\dfrac{19}{60}\right):1\dfrac{23}{24}\)

\(=\dfrac{28}{15}.25.3+\dfrac{13}{60}.\dfrac{24}{47}\)

\(=140+\dfrac{26}{235}=140\dfrac{26}{235}\)

b) \(\dfrac{\left(\dfrac{11^2}{200}+0,414:0,01\right)}{\dfrac{1}{12}-37.25+3\dfrac{1}{6}}\)

\(=\dfrac{\left(\dfrac{121}{200}-41,4\right)}{\dfrac{1}{12}-92519+\dfrac{19}{6}}\)

\(=\dfrac{2\dfrac{191}{207}}{-9251575}\)

\(\dfrac{19}{\dfrac{5}{8}}:\dfrac{7}{2013}-\dfrac{26}{\dfrac{5}{8}}:\dfrac{7}{2013}\)

=\(\dfrac{152}{5}:\dfrac{7}{2013}-\dfrac{13}{20}:\dfrac{7}{2013}\)

=(\(\dfrac{152}{5}-\dfrac{13}{20}\)):\(\dfrac{7}{2013}\)

=(\(\dfrac{608}{20}-\dfrac{13}{20}\)):\(\dfrac{7}{2013}\)

=\(\dfrac{595}{20}:\dfrac{7}{2013}\)

=\(\dfrac{1197735}{40260}:\dfrac{140}{40260}\)

=\(\dfrac{119773}{140}\)

Mình ko chắc cách này đc ko nữa bạn tham khảo thôi nhé. Chúc may mắn.

a)

\(P=\dfrac{5}{6}+\dfrac{5}{12}+\dfrac{5}{20}+\dfrac{5}{30}+\dfrac{5}{42}+\dfrac{5}{56}+\dfrac{5}{72}+\dfrac{5}{90}\\ =\dfrac{5}{2.3}+\dfrac{5}{3.4}+\dfrac{5}{4.5}+\dfrac{5}{5.6}+\dfrac{5}{6.7}+\dfrac{5}{7.8}+\dfrac{5}{8.9}+\dfrac{5}{9.10}\\ \Rightarrow\dfrac{1}{5}P=\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+...+\dfrac{1}{9.10}\\ =\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{9}-\dfrac{1}{10}\\ =\dfrac{1}{2}-\dfrac{1}{10}=\dfrac{5}{10}-\dfrac{1}{10}\\ =\dfrac{4}{10}=\dfrac{2}{5}\\ \Rightarrow P=\dfrac{2}{5}\cdot5=2\)

ta thấy : \(\dfrac{-1003}{-2002}\) = \(\dfrac{1003}{2002}\)

\(\dfrac{1004}{-2003}\) = \(\dfrac{-1004}{2003}\)

Sắp xếp : \(\dfrac{1004}{-2003}\) <\(\dfrac{-1003}{2003}\) <\(\dfrac{-1002}{2003}\) <\(\dfrac{1001}{2002}\) <\(\dfrac{-1003}{-2002}\)