Question

7 numeric 1 point what is the real solution for x for the given equation? \\(\sqrt{5 - x} = \sqrt{x + 1}\\) answer

Explanation:

Step1: Square both sides

$$(\sqrt{5-x})^2 = (\sqrt{x+1})^2$$
$$5 - x = x + 1$$

Step2: Isolate x terms

$$5 - 1 = x + x$$
$$4 = 2x$$

Step3: Solve for x

$$x = \frac{4}{2}$$

Step4: Verify solution

Substitute $x=2$ into original equation:
$\sqrt{5-2}=\sqrt{3}$, $\sqrt{2+1}=\sqrt{3}$, so it is valid.

Answer:

$2$