Алгебра 8 класс учебник Макарычев, Миндюк ответы – номер 990

а) $$ \left\{\begin{array}{l} \frac{x-1}{2}-\frac{x-3}{3}<2\left\{\begin{array}{l} \frac{3(x-1)-2(x-3)}{6}<2 \\ \frac{13 x-1}{2}>0 \end{array}\right. \\ \frac{13 x-1}{2}>0 \end{array}\right. $$ $$ \left\{\begin{array} { l } { \frac { 3 x - 3 - 2 x + 6 } { 6 } < 2 } \\ { \frac { 1 3 x - 1 } { 2 } > 0 } \end{array} \left\{\begin{array} { l } { \frac { x + 3 } { 6 } < 2 } \\ { \frac { 1 3 x - 1 } { 2 } > 0 } \end{array} \left\{\begin{array}{l} x+3<2 · 6 \\ 13 x-1>0 · 2 \end{array}\right.\right.\right. $$ $$ \left\{\begin{array} { l } { x < 1 2 - 3 } \\ { 1 3 x > 0 + 1 } \end{array} \left\{\begin{array} { l } { x < 9 } \\ { 1 3 x > 1 } \end{array} \left\{\begin{array} { l } { x < 9 } \\ { x > 1 : 1 3 } \end{array} \left\{\begin{array}{l} x<9 \\ x>\frac{1}{13} \end{array}\right.\right.\right.\right. $$

    (1/13; 9)
б) $$ \left\{\begin{array} { l } { \frac { 3 x + 1 } { 2 } < - 1 } \\ { \frac { x } { 2 } - 1 < x } \end{array} \left\{\begin{array} { l } { \frac { 3 x + 1 } { 2 } < - 1 } \\ { \frac { x - 2 } { 2 } < x } \end{array} \left\{\begin{array}{l} 3 x+1<-1 · 2 \\ x-2< x · 2 \end{array}\right.\right.\right. $$ $$ \left\{\begin{array} { l } { 3 x < - 2 - 1 } \\ { x - 2 x < 2 } \end{array} \left\{\begin{array} { l } { 3 x < - 3 } \\ { - x < 2 } \end{array} \left\{\begin{array} { l } { x < - 3 : 3 } \\ { x > 2 : ( - 1 ) } \end{array} \left\{\begin{array}{l} x<-1 \\ x>-2 \end{array}\right.\right.\right.\right. $$

    (−2; −1)
в) $$ \left\{\begin{array} { l } { 4 - \frac { y - 1 } { 3 } \geq y } \\ { \frac { 7 y - 1 } { 8 } \geq 6 } \end{array} \left\{\begin{array} { l } { \frac { 1 2 - y + 1 } { 3 } \geq y } \\ { \frac { 7 y - 1 } { 8 } \geq 6 } \end{array} \left\{\begin{array}{l} 13-y \geq 3 · y \\ 7 y-1 \geq 6 · 8 \end{array}\right.\right.\right. $$ $$ \left\{\begin{array} { l } { - y - 3 y \geq - 1 3 } \\ { 7 y \geq 4 8 + 1 } \end{array} \left\{\begin{array} { l } { - 4 y \geq - 1 3 } \\ { 7 y \geq 4 9 } \end{array} \left\{\begin{array} { l } { y \leq - 1 3 : ( - 4 ) } \\ { y \geq 4 9 : 7 } \end{array} \left\{\begin{array}{l} y \leq 3,25 \\ y \geq 7 \end{array}\right.\right.\right.\right. $$

    Решения нет
г) $$ \left\{\begin{array} { l } { \frac { 5 a + 8 } { 3 } - a \geq 2 a } \\ { 1 - \frac { 6 - 1 5 a } { 4 } \geq a } \end{array} \left\{\begin{array} { l } { \frac { 5 a + 8 - 3 a } { 3 } \geq 2 a } \\ { \frac { 4 - 6 + 1 5 a } { 4 } \geq a } \end{array} \left\{\begin{array}{l} \frac{5 a+8-3 a}{3} \geq 2 a \\ \frac{4-6+15 a}{4} \geq a \end{array}\right.\right.\right. $$ $$ \left\{\begin{array} { l } { 2 a + 8 \geq 2 a · 3 } \\ { 1 5 a - 2 \geq a · 4 } \end{array} \left\{\begin{array}{l} 2 a-6 a \geq-8 \\ 15 a-4 a \geq 2 \end{array}\right.\right. $$ $$ \left\{\begin{array} { l } { - 4 a \geq - 8 } \\ { 1 1 a \geq 2 } \end{array} \left\{\begin{array} { l } { a \leq - 8 : ( - 4 ) } \\ { a \geq 2 : 1 1 } \end{array} \left\{\begin{array}{l} a \leq 2 \\ a \geq \frac{2}{11} \end{array}\right.\right.\right. $$

    [2/11; 2]