$\text{ Set of all values of }x\text{ satisfying the equation }|x+1|=5-|x-4|\text{ is }$

$\begin{array}{l}|x+1|=5-|x-4|\\ \Rightarrow |x+1|+|x-4|=5\\ \Rightarrow |x+1|+|x-4|=\left|\right(x+1)+(4-x\left)\right| \left(\sin ce \left|x+y\right|=\left|x\right|+\left|y \right| happens if both x and y are positive or negative i.e xy\ge 0\right)\\ \Rightarrow (x+1)(4-x)\ge 0\\ \Rightarrow (x+1)(x-4)\le 0\\ \Rightarrow x\in [-1,4]\end{array}$