Sure, let's solve the equation step-by-step:
We start with the given equation:
[tex]\[ x + 10 = -15 \][/tex]
To isolate [tex]\( x \)[/tex], we need to get rid of the 10 that is being added to [tex]\( x \)[/tex]. We do this by subtracting 10 from both sides of the equation:
[tex]\[ x + 10 - 10 = -15 - 10 \][/tex]
Simplifying the left side:
[tex]\[ x = -25 \][/tex]
So, we propose that the solution is [tex]\( x = -25 \)[/tex].
Next, we need to check our proposed solution by substituting [tex]\( x = -25 \)[/tex] back into the original equation to see if it satisfies the equation:
Substitute [tex]\( x = -25 \)[/tex] into the original equation:
[tex]\[ -25 + 10 = -15 \][/tex]
Simplify the left side:
[tex]\[ -15 = -15 \][/tex]
Since both sides of the original equation are equal after the substitution, our solution [tex]\( x = -25 \)[/tex] is correct.
Therefore, the correct choice is:
A. The solution set is [tex]\(\{-25\}\)[/tex].
