Question

Solve the following linear inequations and graph the solution set on a real number line.​
$\frac{5}{4}x>1+\frac{1}{3}(4x-1),x\in R$

Answer 1

Finding the solution set of $x$
Given:
$\frac{5}{4}x>1+\frac{1}{3}(4x-1)$

$\frac{5}{4}x-1>\frac{1}{3}(4x-1)$

$3(5x-4)>4(4x-1)$

$15x-12>16x-4$

By taking the like terms to one side of equation,we get,

$-12+4>16x-15x$

$x<-8$

As per the condition given in the question,$x\in R$
Therefore,solution set$x:x<-8$

Set can be represented in number line as,