Реши задание на изображении

Краткий ответ:

1. \(x=\frac14\)
2. \(t=\frac18\)
3. \(b=\frac15\)
4. \(y=\frac14\)
5. \(a=\frac18\)
6. \(p=0\)
7. \(b=\frac16\)
8. \(c=\frac16\)

Решение

1)
\[ x+\frac23=\frac34+\frac16 \] \[ x=\frac34+\frac16-\frac23 =\frac9{12}+\frac2{12}-\frac8{12} =\frac3{12}=\frac14 \]

2)
\[ \left(\frac38-t\right)+\frac12=\frac34 \] \[ \frac38+\frac48-t=\frac68 \] \[ \frac78-t=\frac68,\qquad t=\frac18 \]

3)
\[ \frac65-\left(b+\frac23\right)=\frac13 \] Перенесём скобки: \[ b+\frac23=\frac65-\frac13=\frac{18}{15}-\frac5{15}=\frac{13}{15} \] \[ b=\frac{13}{15}-\frac{10}{15}=\frac3{15}=\frac15 \]

4)
\[ \frac34+\left(\frac25-y\right)=\frac9{10} \] \[ \frac25-y=\frac9{10}-\frac34=\frac{18}{20}-\frac{15}{20}=\frac3{20} \] \[ -y=\frac3{20}-\frac8{20}=-\frac5{20} \] \[ y=\frac14 \]

5)
\[ a+\frac16=\frac{11}{12}-\frac58 \] \[ a+\frac16=\frac{22}{24}-\frac{15}{24}=\frac7{24} \] \[ a=\frac7{24}-\frac4{24}=\frac3{24}=\frac18 \]

6)
\[ \left(\frac35+p\right)+\frac1{15}=\frac23 \] \[ p=\frac{10}{15}-\frac9{15}-\frac1{15}=0 \]

7)
\[ \frac{11}{21}-b=\frac3{14}+\frac17 \] \[ \frac3{14}+\frac17=\frac3{14}+\frac2{14}=\frac5{14} \] \[ b=\frac{11}{21}-\frac5{14} =\frac{22}{42}-\frac{15}{42} =\frac7{42}=\frac16 \]

8)
\[ \frac45-c=\frac{14}{15}-\frac3{10} \] \[ \frac45-c=\frac{28}{30}-\frac9{30}=\frac{19}{30} \] \[ c=\frac{24}{30}-\frac{19}{30}=\frac5{30}=\frac16 \]

Проверка выполняется подстановкой: например, в № 6
\[ \left(\frac35+0\right)+\frac1{15} =\frac9{15}+\frac1{15} =\frac{10}{15}=\frac23. \] Значит, ответы найдены верно.