Solve each of the following system of equations in R.

|4–x|+1<3

Subtracting 1 from both the sides.

⇒ |4–x|+1–1<3–1

⇒ |4–x|<2

We know that,

|a–x|<r ⟺ a–r<x<a+r

Here, a=4 and r=2

⇒ 4–2<x<4+2

⇒2<x<6

**⇒** **x** **ϵ****(2, 6)**

We can verify the answers using graph as well.

2