Let's analyze and solve the equation step-by-step to determine the number of solutions for [tex]\( 5 - x = -2 \)[/tex].
### Step-by-Step Solution:
1. Start with the given equation:
[tex]\[
5 - x = -2
\][/tex]
2. Isolate the variable [tex]\( x \)[/tex]:
To isolate [tex]\( x \)[/tex], we need to get the [tex]\( x \)[/tex]-term by itself on one side of the equation. We'll first subtract 5 from both sides:
[tex]\[
5 - x - 5 = -2 - 5
\][/tex]
Simplifying both sides, we get:
[tex]\[
-x = -7
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
To solve for [tex]\( x \)[/tex], we need to get rid of the negative sign in front of [tex]\( x \)[/tex]. We do this by multiplying both sides of the equation by -1:
[tex]\[
-1 \cdot (-x) = -1 \cdot (-7)
\][/tex]
Simplifying both sides, we get:
[tex]\[
x = 7
\][/tex]
### Conclusion:
By solving the equation [tex]\( 5 - x = -2 \)[/tex], we find that [tex]\( x = 7 \)[/tex].
This is a single solution, which means the equation has a unique solution. Therefore, the number of solutions to the equation [tex]\( 5 - x = -2 \)[/tex] is:
[tex]\[
\text{Unique solution}
\][/tex]
