`2/3x-3/2x=5/12`

`=>-5/6x=5/12`

`=>x=-1/2`

Vậy `x=-1/2`

2/3x-3/2x=5/12

x.(2/3-3/2)=5/12

x.-5/6     =5/12

     x       =5/12:-5/6

     x       =-1/2

Áp dụng tính chất của dãy tỉ số bằng nhau, ta được:

\(\dfrac{x}{4}=\dfrac{y}{5}=\dfrac{x+y}{4+5}=\dfrac{18}{9}=2\)

Do đó: x=8; y=10

a) \(\dfrac{2}{3}+\dfrac{3}{4}< x< 1\dfrac{1}{3}+\dfrac{4}{5}\)

\(\dfrac{2\times4}{3\times4}+\dfrac{3\times3}{4\times3}< x< \dfrac{\left(1\times3+1\right)\times5}{3\times5}+\dfrac{4\times3}{5\times3}\)

\(\dfrac{8}{12}+\dfrac{9}{12}< x< \dfrac{20}{15}+\dfrac{12}{15}\\ \dfrac{17}{12}< x< \dfrac{32}{15}\)

Ước tính: \(\dfrac{17}{12}=1,4\) và \(\dfrac{32}{15}=2,1\). Vậy số tự nhiên x = 2 sẽ thõa mãn 1,4 < x < 2,1

b)

 \(\dfrac{5}{6}-\dfrac{1}{4}< x< 2\dfrac{1}{3}-\dfrac{2}{5}\\ \dfrac{5\times4}{6\times4}-\dfrac{1\times6}{4\times6}< x< \dfrac{\left(2\times3+1\right)\times5}{3\times5}-\dfrac{2\times3}{5\times3}\\ \dfrac{20}{24}-\dfrac{6}{24}< x< \dfrac{35}{15}-\dfrac{6}{15}\\ \dfrac{14}{24}< x< \dfrac{29}{15}\)

Ước tính \(\dfrac{14}{24}=0,5\) và \(\dfrac{29}{15}=1,9\)

Vậy với x là số tự nhiên x = 1 sẽ thõa mãn 0,5 < x < 1,9

a) với a = -2 ta được phương trình:

3.[(-2) - 2].x + 2.(-2).(x - 1) = 4.(-2) + 3

<=> 3.(-4x) - 4.(x - 1) = (-8) + 3

<=> -12x - 4(x - 1) = -5

<=> -12x - 4x + 4 = -5

<=> -16x + 4 = -5

<=> -16x = -5 - 4

<=> -16x = -9

<=> x = 9/16

b) để x = 1, ta có:

3.(a - 2).1 + 2a(1 - 1) = 4a + 3

<=> 3(a - 2) + 0 = 4a + 3

<=> 3a - 6 = 4a + 3

<=> 3a - 6 - 4a = 3

<=> -a - 6 = 3

<=> -a = 3 + 6

<=> a = -9

6/21-(−12/44)+10/14−(1/(−4))−18/33

=2/7+12/44+5/7−((−1)/4)−6/11=2/7+12/44+5/7−((−1)/4)−6/11

=2/7+3/11+5/7+1/4−6/11=2/7+3/11+5/7+1/4−6/11

=(3/11−6/11)+(2/7+5/7)+1/4=(3/11−6/11)+(2/7+5/7)+1/4

=−3/11+7/7+1/4=−3/11+7/7+1/4

=43/44

8 It took me 3 hours to do these exercise

9 Many years ago, my village used to be very poor

10 Mary last met him 5 years ago

11 Would you mind giving me a hand

12 There used to be many old buildings in this city

13 When were they married

14 I started learning Japanese 2 years ago

15 Jack used to be a good student

16  My sister used to buy all her clothes in Henry's

17 Braille is reading system for the blind

\(\left\{{}\begin{matrix}x\ne-\dfrac{5}{3}\\-\dfrac{2}{3x+5}>0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ne-\dfrac{5}{3}\\3x+5< 0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ne-\dfrac{5}{3}\\x< -\dfrac{5}{3}\end{matrix}\right.\Leftrightarrow x< -\dfrac{5}{3}\)

\(\sqrt{\dfrac{72x}{128}}=\dfrac{3}{4}\)

\(\Leftrightarrow x\cdot\dfrac{9}{16}=\dfrac{9}{16}\)

hay x=1