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Solve the equation. Be sure to check your proposed solution by substituting it for the variable in the original equation.

[tex]\[ x + 10 = -15 \][/tex]

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. The solution set is [tex]\(\{\square\}\)[/tex]. (Type an integer or a simplified fraction.)
B. The solution set is [tex]\(\{x \mid x \text{ is a real number}\}\)[/tex].
C. The solution set is [tex]\(\varnothing\)[/tex].

Sagot :

GinnyAnsweridn
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].
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