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Linear Inequations

Solve the linear inequation and represent the solution set on a number line:
3(x7)157x>(x+13),xR


Consider 3(x7)157x

i.e. 3x+21157x

i.e. 4x6

i.e. x32 32x (1)

Consider 157x>x+13

i.e. 4521x>x+1

i.e. 44>22x

i.e. 2>x x<2 (2)

We have from equations (1) and (2), \;\; - \dfrac{3}{2} \leq x < 2

\therefore \; The solution set of the given inequation is: \; \left\{x \mid -\dfrac{3}{2} \leq x < 2, \; x \in R \right\}