Question

solve the equation 2x -5<5x+4<11,where x€1​

Answer 1

EXPLANATION :

$\star \: \: \: { \underline\blue {Given}} :$

${\sf{2x - 5 < 5x + 4 < 11}}$

$\star \: \: {\underline{ \blue{Solution}}} :$

$\sf \: 2x - 5 < 11$

$\sf \implies \: x < 3$

${{x \in \: ( - \infty ,3)}} \underline{ \: \: \: \: \: \: \: \: \: }(1)$

Again,

$\sf \: 5x + 4 < 11$

$\sf \implies \: x < \frac{7}{5}$

$x \in \:( - \infty , \frac{7}{5} ) \underline{ \: \: \: \: \: \: \: \: }(2)$

From 1 and 2

${ \boxed{ \tt\: x \in \: ( \frac{7}{5} ,3)}}$