Answer
$x=4$
Work Step by Step
Given equation-
$\sqrt {5-x} +1$ = $x-2$
i.e. $\sqrt {5-x} -x+3$ = $0$
We are asked to find all real solutions of this equation.
Graphing $\sqrt {5-x} -x+3$, using graphing calculator-
We get one x−intercept, i.e. $x=4$
Therefore $x=4$