Question

Answer 1

1.

$4-|x-\frac{1}{5}|=\frac{-1}{2}$

$|x-\frac{1}{5}|=4-\frac{-1}{2}=\frac{9}{2}$

\(\Rightarrow \left[\begin{matrix} x-\frac{1}{5}=\frac{9}{2}\\ x-\frac{1}{5}=\frac{-9}{2}\end{matrix}\right.\Leftrightarrow \left[\begin{matrix} x=\frac{47}{10}\\ x=\frac{-43}{10}\end{matrix}\right.\)

2.

$(2x+3)^2=\frac{4}{81}=(\frac{2}{9})^2=(\frac{-2}{9})^2$

\(\Rightarrow \left[\begin{matrix} 2x+3=\frac{2}{9}\\ 2x+3=\frac{-2}{9}\end{matrix}\right.\Leftrightarrow \left[\begin{matrix} x=\frac{-25}{18}\\ x=\frac{-29}{18}\end{matrix}\right.\)

3.

$\frac{3}{4}-|\frac{1}{2}x-1|=\frac{1}{2}$

$|\frac{1}{2}x-1|=\frac{1}{4}$

\(\Rightarrow \left[\begin{matrix} \frac{1}{2}x-1=\frac{1}{4}\\ \frac{1}{2}x-1=\frac{-1}{4}\end{matrix}\right.\Leftrightarrow \left[\begin{matrix} x=\frac{5}{2}\\ x=\frac{3}{2}\end{matrix}\right.\)

 

Answer 2

4.

$\frac{3}{4}+\frac{1}{4}:x=\frac{2}{5}$
$\frac{1}{4}:x=\frac{2}{5}-\frac{3}{4}=\frac{-7}{20}$

$x=\frac{1}{4}:\frac{-7}{20}=\frac{-5}{7}$

Answer 3

5.

$\frac{|-2x|}{10}=\frac{3}{5}$

$|-2x|=\frac{3}{5}.10=6$

$|-x|=3$

$\Rightarrow -x=\pm 3$

$\Rightarrow x=3$ hoặc $x=-3$

Answer 4

6.

Áp dụng tính chất dãy tỉ số bằng nhau:

$\frac{x}{12}=\frac{y}{3}=\frac{x-y}{12-3}=\frac{18}{9}=2$
$\Rightarrow x=12.2=24; y=2.3=6$

 

Answer 5

7.

$2,5:\frac{1}{3}=x:\frac{2}{5}$

$\frac{15}{2}=x:\frac{2}{5}$

$x=\frac{15}{2}.\frac{2}{5}=3$

 

Answer 6

8.

$\frac{x}{2}=\frac{y}{5}; \frac{y}{3}=\frac{z}{7}$

$\Rightarrow \frac{x}{6}=\frac{y}{15}=\frac{z}{35}$

Áp dụng tính chất dãy tỉ số bằng nhau:

$\frac{x}{6}=\frac{y}{15}=\frac{z}{35}=\frac{x+y+z}{6+15+35}=\frac{-56}{56}=-1$

$\Rightarrow x=6.(-1)=-6; y=15(-1)=-15; z=35.(-1)=-35$

Answer 7

9.

$4x=3y\Rightarrow \frac{x}{3}=\frac{y}{4}$

$7y=5z\Rightarrow \frac{y}{5}=\frac{z}{7}$

$\Rightarrow \frac{x}{15}=\frac{y}{20}=\frac{z}{28}$

Áp dụng tính chất dãy tỉ số bằng nhau thì:

$\frac{x}{15}=\frac{y}{20}=\frac{z}{28}=\frac{x-y+z}{15-20+28}=\frac{-46}{23}=-2$

$\Rightarrow x=15(-2)=-30; y=20(-2)=-40; z=28(-2)=-56$