Реши все так как на второй фотки

Краткие ответы:

1. \(x=\frac59\)
2. \(x=\frac{17}{5}\)
3. \(x=\frac43\)
4. \(x=\frac{21}{5}\)
5. \(x=3\)
6. \(x=\frac43\)
7. \(x=\frac92\)
8. \(x=\frac{36}{37}\)
9. \(x=\frac94\)
10. \(x=\frac32\)
11. \(x=-\frac{16}{5}\)
12. \(x=\frac95\)
13. \(x=-\frac{18}{5}\)
14. \(x=\frac{37}{6}\)
15. \(x=\frac{27}{2}\)
16. \(x=\frac{32}{25}\)
17. \(x=\frac35\)
18. \(x=\frac{124}{15}\)
19. \(x=10\)
20. \(x=\frac{11}{4}\)

Во второй фотографии показано решение системы методом подстановки, а здесь даны отдельные уравнения с одной переменной. Поэтому используем такой порядок:

1. Раскрываем скобки.
2. Переносим слагаемые с \(x\) в одну сторону, числа — в другую.
3. Приводим подобные слагаемые.
4. Делим на коэффициент при \(x\).

Пошаговое решение

1.

\[ \begin{aligned} 0{,}4x+\frac23&=\frac56+0{,}1x,\\ 0{,}4x-0{,}1x&=\frac56-\frac23,\\ 0{,}3x&=\frac16,\\ x&=\frac16\cdot\frac{10}{3}=\frac59. \end{aligned} \]

2.

\[ \begin{aligned} \frac34(x-0{,}8)&=\frac12x+0{,}25,\\ \frac34x-\frac35&=\frac12x+\frac14,\\ \left(\frac34-\frac12\right)x&=\frac14+\frac35,\\ \frac14x&=\frac{17}{20},\\ x&=\frac{17}{5}. \end{aligned} \]

3.

\[ \begin{aligned} \frac58x-0{,}3&=\frac14x+\frac15,\\ \left(\frac58-\frac14\right)x&=\frac3{10}+\frac15,\\ \frac38x&=\frac12,\\ x&=\frac12\cdot\frac83=\frac43. \end{aligned} \]

4.

\[ \begin{aligned} 2{,}1+\frac37x&=1{,}5+\frac47x,\\ 2{,}1-1{,}5&=\left(\frac47-\frac37\right)x,\\ 0{,}6&=\frac17x,\\ x&=4{,}2=\frac{21}{5}. \end{aligned} \]

5.

\[ \begin{aligned} \frac79x-\frac13&=0{,}6x+0{,}2,\\ \left(\frac79-\frac35\right)x&=\frac13+\frac15,\\ \frac8{45}x&=\frac8{15},\\ x&=3. \end{aligned} \]

6.

\[ \begin{aligned} 0{,}75x-\frac25&=\frac38x+0{,}1,\\ \left(\frac34-\frac38\right)x&=\frac25+\frac1{10},\\ \frac38x&=\frac12,\\ x&=\frac43. \end{aligned} \]

7.

\[ \begin{aligned} \frac45(0{,}5x+1)&=\frac23x-0{,}4,\\ \frac25x+\frac45&=\frac23x-\frac25,\\ \left(\frac23-\frac25\right)x&=\frac45+\frac25,\\ \frac4{15}x&=\frac65,\\ x&=\frac65\cdot\frac{15}{4}=\frac92. \end{aligned} \]

8.

\[ \begin{aligned} 1{,}2x+\frac3{10}&=\frac7{12}x+0{,}9,\\ \left(\frac65-\frac7{12}\right)x&=\frac9{10}-\frac3{10},\\ \frac{37}{60}x&=\frac35,\\ x&=\frac35\cdot\frac{60}{37}=\frac{36}{37}. \end{aligned} \]

9.

\[ \begin{aligned} \frac56x-0{,}25&=\frac23x+\frac18,\\ \left(\frac56-\frac23\right)x&=\frac14+\frac18,\\ \frac16x&=\frac38,\\ x&=\frac94. \end{aligned} \]

10.

\[ \begin{aligned} 0{,}6\left(x+\frac13\right)&=0{,}4x+\frac12,\\ \frac35x+\frac15&=\frac25x+\frac12,\\ \left(\frac35-\frac25\right)x&=\frac12-\frac15,\\ \frac15x&=\frac3{10},\\ x&=\frac32. \end{aligned} \]

11.

\[ \begin{aligned} \frac35x+0{,}12&=\frac12(x-0{,}4),\\ \frac35x+\frac3{25}&=\frac12x-\frac15,\\ \left(\frac35-\frac12\right)x&=-\frac15-\frac3{25},\\ \frac1{10}x&=-\frac8{25},\\ x&=-\frac{16}{5}. \end{aligned} \]

12.

\[ \begin{aligned} 1{,}8-\frac27x&=0{,}9+\frac3{14}x,\\ \left(\frac27+\frac3{14}\right)x&=1{,}8-0{,}9,\\ \frac12x&=\frac9{10},\\ x&=\frac95. \end{aligned} \]

13.

\[ \begin{aligned} \frac5{12}x+0{,}2&=\frac13x-\frac1{10},\\ \left(\frac5{12}-\frac13\right)x&=-\frac1{10}-\frac15,\\ \frac1{12}x&=-\frac3{10},\\ x&=-\frac{18}{5}. \end{aligned} \]

14.

\[ \begin{aligned} 0{,}3x+\frac7{15}&=\frac25x-0{,}15,\\ \left(\frac25-\frac3{10}\right)x&=\frac7{15}+\frac3{20},\\ \frac1{10}x&=\frac{37}{60},\\ x&=\frac{37}{6}. \end{aligned} \]

15.

\[ \begin{aligned} \frac89x-0{,}5&=\frac56x+\frac14,\\ \left(\frac89-\frac56\right)x&=\frac12+\frac14,\\ \frac1{18}x&=\frac34,\\ x&=\frac{27}{2}. \end{aligned} \]

16.

\[ \begin{aligned} 2{,}4-\frac38x&=1{,}6+\frac14x,\\ \left(\frac38+\frac14\right)x&=2{,}4-1{,}6,\\ \frac58x&=\frac45,\\ x&=\frac45\cdot\frac85=\frac{32}{25}. \end{aligned} \]

17.

\[ \begin{aligned} \frac23(x-0{,}6)+0{,}1&=\frac12x-\frac15,\\ \frac23x-\frac25+\frac1{10}&=\frac12x-\frac15,\\ \frac23x-\frac3{10}&=\frac12x-\frac15,\\ \left(\frac23-\frac12\right)x&=-\frac15+\frac3{10},\\ \frac16x&=\frac1{10},\\ x&=\frac35. \end{aligned} \]

18.

\[ \begin{aligned} 0{,}25x+\frac59&=\frac13x-0{,}3+\frac16,\\ \frac14x+\frac59&=\frac13x-\frac3{10}+\frac16,\\ \frac14x+\frac59&=\frac13x-\frac2{15},\\ \left(\frac13-\frac14\right)x&=\frac59+\frac2{15},\\ \frac1{12}x&=\frac{31}{45},\\ x&=\frac{124}{15}. \end{aligned} \]

19.

\[ \begin{aligned} \frac7{10}x-\left(0{,}4+\frac15\right)&=\frac34x-1{,}1,\\ \frac7{10}x-\frac35&=\frac34x-\frac{11}{10},\\ \left(\frac34-\frac7{10}\right)x&=\frac{11}{10}-\frac35,\\ \frac1{20}x&=\frac12,\\ x&=10. \end{aligned} \]

20.

\[ \begin{aligned} 1{,}5\left(\frac23x-0{,}2\right)&=0{,}8x+\frac14,\\ \frac32\left(\frac23x-\frac15\right)&=\frac45x+\frac14,\\ x-\frac3{10}&=\frac45x+\frac14,\\ \frac15x&=\frac14+\frac3{10},\\ \frac15x&=\frac{11}{20},\\ x&=\frac{11}{4}. \end{aligned} \]

Проверка, например № 1: \[ 0{,}4\cdot\frac59+\frac23 =\frac29+\frac69 =\frac89, \] \[ \frac56+0{,}1\cdot\frac59 =\frac{15}{18}+\frac1{18} =\frac89. \] Левая и правая части совпали. Остальные ответы проверяются подстановкой таким же способом.