$$ \left. \begin{array} { l } { \left\{ \begin{array} { l } { 2 x - 5 \leq 3 , } \ { 0,3 x \geq - 21 . } \end{array} ight.} \ { \left\{ \begin{array} { l l } { 5 x - 2 \geq - 12 , } \ { 0,5 x \leq 4 . } \end{array} ight.} \end{array} ight. \quad \left\{ \begin{array} { l } { \frac { x + 2 } { 4 } + \frac { x + 3 } { 2 } 3 , } \ { - x - 2

Question

$$ \left. \begin{array} { l } { \left\{ \begin{array} { l } { 2 x - 5 \leq 3 , } \ { 0,3 x \geq - 21 . } \end{array} ight.} \ { \left\{ \begin{array} { l l } { 5 x - 2 \geq - 12 , } \ { 0,5 x \leq 4 . } \end{array} ight.} \end{array} ight. \quad \left\{ \begin{array} { l } { \frac { x + 2 } { 4 } + \frac { x + 3 } { 2 } > 3 , } \ { - x - 2 < - 3 . } \end{array} \quad \left\{ \begin{array} { l } { ( x + 5 ) ( x + 2 ) < 0 , } \ { ( x + 2 ) ( x - 6 ) < 0 . } \ { \frac { x - 1 } { 2 } - \frac { x - 17 } { 4 } \geq 5 , } \ { 2 x - 3,5 > 7 . } \end{array} , \left\{ \begin{array} { l } { \frac { x - 7 } { x + 2 } < 0 , } \ { x ^ { 2 } - 4 x - 5 > 0 ; } \end{array} ight. ight. ight. $$

Rojas Matthews · Accepted Answer

Solutions to the inequalities are: - $$ x = 4 $$ or $$ x = -70 $$ - $$ x = -2 $$ or $$ x = 8 $$ - $$ x > \frac{4}{3} $$ and $$ x = 1 $$ - $$ -5 < x < -2 $$, $$ -2 < x < 6 $$, $$ x \geq 5 $$, $$ x > 5.25 $$ - $$ -2 < x < 7 $$ and $$ x < -1 $$ or $$ x > 5 $$ Combining these, the overall solution set is determined by the overlapping ranges of the individual solutions.

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