Solve the linear inequation and represent the solution set on a number line:
−3(x−7)≥15−7x>(x+13),x∈R
Consider −3(x−7)≥15−7x
i.e. −3x+21≥15−7x
i.e. 4x≥−6
i.e. x≥−32 ⟹ −32≤x ⋯(1)
Consider 15−7x>x+13
i.e. 45−21x>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\}