For the following inequations, graph the solution set on the real number line :

x - 1 < 3 - x ≤ 5

x - 1 < 3 - x ≤ 5

Solving L.H.S. of the equation,

⇒ x - 1 < 3 - x

⇒ x + x < 3 + 1

⇒ 2x < 4

⇒ x < 2 ………(i)

Solving R.H.S. of the equation,

⇒ 3 - x ≤ 5

⇒ x ≥ 3 - 5

⇒ x ≥ -2 ………(ii)

From (i) and (ii) we get,

-2 ≤ x < 2.

∴ Solution set = {-2 ≤ x < 2 : x ∈ R}

Solution on the number line is :