Tìm x biết

1.3/4+1/5:x=1/4

2.-2x-2/3(3/4-1/8x)=(-1/2)^3

3.(3x+2)(5-x^2)=0

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

5.|x-2/3|-2/5=1/3

6.|x-2|-|1-2x|=0

7.2.3^x-405=3^x-1

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Đáp án:

Giải thích các bước giải:

 1.  $\frac{3}{4}$ + $\frac{1}{5}$ : x = $\frac{1}{4}$ 

$\frac{1}{5}$ : x = $\frac{1}{4}$  - $\frac{3}{4}$

$\frac{1}{5}$ : x = $\frac{-1}{2}$

x = $\frac{1}{5}$ : $\frac{-1}{2}$

x = $\frac{-2}{5}$ 

2. -2x - $\frac{2}{3}$($\frac{3}{4}$ - $\frac{1}{8}$x) = $(\frac{-1}{2})^{3}$

-2x - $\frac{1}{2}$ - $\frac{1}{12}$x = $\frac{-1}{8}$

-2x - $\frac{1}{2}$ = $\frac{-1}{8}$ + $\frac{1}{12}$x

-2x - $\frac{1}{12}$x = $\frac{-1}{8}$ + $\frac{1}{2}$

$\frac{25}{12}$x = $\frac{3}{8}$

x = $\frac{3}{8}$ : $\frac{25}{12}$

x = $\frac{9}{50}$

3.  (3x + 2)(5-$x^{2}$)=0

\(\left[ \begin{array}{l}3x+2=0\\ 5-$x^{2}$ = 0\end{array} \right.\)

\(\left[ \begin{array}{l}3x=-2\\$x^{2}$ = 5 \end{array} \right.\)

\(\left[ \begin{array}{l}x=$\frac{-2}{3}$ \\x=$\sqrt{5}$ \end{array} \right.\)

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

|x-1| - $\frac{1}{12}$ = 2

|x-1| = 2 + $\frac{1}{12}$ 

|x - 1| = $\frac{25}{12}$ 

\(\left[ \begin{array}{l}x - 1 = $\frac{25}{12}$ \\x - 1 = $\frac{-25}{12}$\end{array} \right.\)

\(\left[ \begin{array}{l}x=$\frac{37}{12}$ \\x=$\frac{-13}{12}$\end{array} \right.\)

5. |x - $\frac{2}{3}$| - $\frac{-2}{5}$ = $\frac{1}{3}$

|x - $\frac{2}{3}$| = $\frac{1}{3}$ + $\frac{-2}{5}$

|x - $\frac{2}{3}$| = $\frac{1}{15}$

\(\left[ \begin{array}{l}x - $\frac{2}{3}$ = $\frac{1}{15}$\\2 - $\frac{2}{3}$ = $\frac{-1}{15}$\end{array} \right.\)

\(\left[ \begin{array}{l}x=$\frac{11}{15}$ \\x=$\frac{3}{5}$ \end{array} \right.\)

6. |x-2| - |1-2x| = 0

\(\left[ \begin{array}{l}x - 2 = 0\\1 - 2x = 0\end{array} \right.\)

\(\left[ \begin{array}{l}x=2\\2x=1\end{array} \right.\)

\(\left[ \begin{array}{l}x=2\\x=$\frac{1}{2}$ \end{array} \right.\)

7. 2 . $3^{x}$  - 405 = $3^{x-1}$

2 .  $3^{x}$  - 405 = $3^{x}$ . $\frac{1}{3}$ 

2 .  $3^{x}$ - $3^{x}$ . $\frac{1}{3}$ =405

$3^{x}$ . (2 - $\frac{1}{3}$) = 405

$3^{x}$ . $\frac{5}{3}$ = 405

$3^{x}$ = 405 : $\frac{5}{3}$ 

$3^{x}$ = 243

$3^{x}$ = $3^{5}$

x=5