Question

Answer 1

1. 

$(x+\frac{1}{5})^2+\frac{17}{25}=\frac{26}{25}$

$(x+\frac{1}{5})^2=\frac{26}{25}-\frac{17}{25}$

$(x+\frac{1}{5})^2=\frac{9}{25}=(\frac{3}{5})^2=(\frac{-3}{5})^2$

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

Answer 2

2. 

\((\frac{1}{2}-x)^2:\frac{9}{11}=\frac{11}{4}\)

\((\frac{1}{2}-x)^2=\frac{11}{4}.\frac{9}{11}=\frac{9}{4}=(\frac{3}{2})^2=(\frac{-3}{2})^2\)

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

 

Answer 3

3.

\((\frac{1}{2}+\frac{1}{3}):x^3=\frac{-5}{6}\)

\(\frac{5}{6}:x^3=\frac{-5}{6}\)

\(x^3=\frac{5}{6}:\frac{-5}{6}=-1=(-1)^3\)

\(x=-1\)

Answer 4

4.

\((11x-\frac{3}{4})^3+21\frac{9}{17}=29\frac{9}{17}\)

\((11x-\frac{3}{4})^3=29\frac{9}{17}-21\frac{9}{17}=8=2^3\)

\(11x-\frac{3}{4}=2\)

\(11x=2+\frac{3}{4}=\frac{11}{4}\)

\(x=\frac{1}{4}\)

Answer 5

5.

$1\frac{5}{27}-(3|x|-\frac{7}{9})^3=\frac{24}{27}$

$(3|x|-\frac{7}{9})^3=1\frac{5}{27}-\frac{24}{27}=\frac{8}{27}=(\frac{2}{3})^3$

$3|x|-\frac{7}{9}=\frac{2}{3}$

$3|x|=\frac{13}{9}$

$|x|=\frac{13}{27}$

$\Rightarrow x=\pm \frac{13}{27}$

Answer 6

6.

$\frac{8}{9}x-\frac{2}{3}=\frac{1}{3}x+1\frac{1}{3}$

$\frac{8}{9}x-\frac{1}{3}x=1\frac{1}{3}+\frac{2}{3}$

$\frac{5}{9}x=2$

$x=\frac{18}{5}$

Answer 7

7.

$x-25\text{%}x-\frac{1}{2}x=-1\frac{1}{4}$

$x-0,25x-0,5x=-1\frac{1}{4}$

$x(1-0,25-0,5)=-1\frac{1}{4}$

$x.0,25=-1\frac{1}{4}$

$x=-5$

Answer 8

8.

$x^3-\frac{4}{25}x=0$

$x(x^2-\frac{4}{25})=0$

\(\Rightarrow \left[\begin{matrix} x=0\\ x^2-\frac{4}{25}=0\end{matrix}\right.\Leftrightarrow \left[\begin{matrix} x=0\\ x^2=(\frac{2}{5})^2=(\frac{-2}{5})^2\end{matrix}\right.\)

\(\Leftrightarrow \left[\begin{matrix} x=0\\ x=\frac{2}{5}\\ x=\frac{-2}{5}\end{matrix}\right.\)

Answer 9

9.

$8\frac{1}{2}-|2x-\frac{3}{4}|=-1\frac{3}{4}$

$|2x-\frac{3}{4}|=8\frac{1}{2}+1\frac{3}{4}=\frac{41}{4}$

\(\Rightarrow \left[\begin{matrix} 2x-\frac{3}{4}=\frac{41}{4}\\ 2x-\frac{3}{4}=-\frac{41}{4}\end{matrix}\right.\Leftrightarrow \left[\begin{matrix} x=\frac{11}{2}\\ x=\frac{-19}{4}\end{matrix}\right.\)

Answer 10

10.

$\frac{x-3}{x-5}=(\frac{-3}{5})^2=\frac{9}{25}$

$\Rightarrow 25(x-3)=9(x-5)$

$\Leftrightarrow 16x=30$

$x=\frac{15}{8}$