Question:
Solve each of the following in equations and represent the solution set on the number line.
$\frac{5 x}{4}-\frac{4 x-1}{3}>1$, where $x \in \mathbf{R}$
Solution:
Given:
$\frac{5 x}{4}-\frac{4 x-1}{3}>1$, where $x \in R$
$\frac{3(5 x)-4(4 x-1)}{12}>1$
$\frac{15 x-16 x+4}{12}>1$
$\frac{-x+4}{12}>1$
Now, multiplying by 12 on both the sides in the above equation,
$\left(\frac{-x+4}{12}\right) \cdot(12)>1$. (12)
$-x+4>12$
Now, subtracting 4 from both the sides in above equation
$-x+4-4>12-4$
$-x>8$
Multiplying by -1 on both the sides of the above equation
$x<-8$
