Question

for what values of the variable does each of the following expressions make sense?
sqaure root of -(6-x)

Answer 1

The expression \( \sqrt{-(6 - x)} \) involves a square root, and for the square root to be defined in the real number system, the expression inside the square root must be non-negative. Therefore, we need to ensure that:

\[
-(6 - x) \geq 0
\]

This can be rearranged as follows:

1. Multiply both sides by -1 (remember to reverse the inequality sign):
\[
6 - x \leq 0
\]

2. Rearranging gives:
\[
6 \leq x
\]
or
\[
x \geq 6
\]

Thus, the expression \( \sqrt{-(6 - x)} \) is defined for values of \( x \) that are greater than or equal to 6.

In interval notation, the solution is:
\[
[6, \infty)
\]