Question

Solve each equation
5 minus square root of 3-x =-2

Answer 1

To solve the equation

\[
5 - \sqrt{3 - x} = -2,
\]

let's isolate the square root term:

1. Subtract 5 from both sides:

\[
-\sqrt{3 - x} = -2 - 5,
\]
\[
-\sqrt{3 - x} = -7.
\]

2. Multiply both sides by -1:

\[
\sqrt{3 - x} = 7.
\]

3. Now, square both sides to eliminate the square root:

\[
3 - x = 49.
\]

4. Rearranging gives:

\[
-x = 49 - 3,
\]
\[
-x = 46.
\]

5. Multiply both sides by -1 to solve for \( x \):

\[
x = -46.
\]

Now, let’s check if this value satisfies the original equation:

Substituting \( x = -46 \) back into the original equation:

\[
5 - \sqrt{3 - (-46)} = 5 - \sqrt{3 + 46} = 5 - \sqrt{49} = 5 - 7 = -2.
\]

This is true!

Thus, the solution to the equation is

\[
\boxed{-46}.
\]