We need to determine which of the provided equations is correctly solved for [tex]\( x \)[/tex]. Let's analyze each option step-by-step.
### Option 1: [tex]\( x + 7 = 12 \)[/tex]
1. To isolate [tex]\( x \)[/tex], subtract 7 from both sides:
[tex]\[
x + 7 - 7 = 12 - 7
\][/tex]
2. Simplify to get:
[tex]\[
x = 5
\][/tex]
3. Check by substituting [tex]\( x = 5 \)[/tex] into the equation:
[tex]\[
5 + 7 = 12
\][/tex]
[tex]\[
12 = 12
\][/tex]
4. This is a valid solution.
### Option 2: [tex]\( x + 5 = 7 \)[/tex]
1. To isolate [tex]\( x \)[/tex], subtract 5 from both sides:
[tex]\[
x + 5 - 5 = 7 - 5
\][/tex]
2. Simplify to get:
[tex]\[
x = 2
\][/tex]
3. Check by substituting [tex]\( x = 2 \)[/tex] into the equation:
[tex]\[
2 + 5 = 7
\][/tex]
[tex]\[
7 = 7
\][/tex]
4. This is a valid solution.
### Option 3: [tex]\( x = 5 + 7 \)[/tex]
1. Simplify the right-hand side:
[tex]\[
x = 12
\][/tex]
2. This equation does not need further verification since it directly provides the value of [tex]\( x \)[/tex]. However, note that this equation does not represent the format typical for solving standard linear equations of the form "ax + b = c" used in the problem context.
### Option 4: [tex]\( x + 7 = 5 \)[/tex]
1. To isolate [tex]\( x \)[/tex], subtract 7 from both sides:
[tex]\[
x + 7 - 7 = 5 - 7
\][/tex]
2. Simplify to get:
[tex]\[
x = -2
\][/tex]
3. Check by substituting [tex]\( x = -2 \)[/tex] into the equation:
[tex]\[
-2 + 7 = 5
\][/tex]
[tex]\[
5 = 5
\][/tex]
4. This is a valid solution.
Given the options and their validations, Options 1, 2, and 4 correctly solve their respective linear equations. However, if we consider valid linear equation formats typically used in such questions, we prefer those that strictly follow the linear form [tex]\( x + a = b \)[/tex].
Therefore, the best choice considering all aspects is:
[tex]\[ x + 7 = 12 ; x = 5 \][/tex]
Hence, the correct answer is:
[tex]\[ \boxed{1} \][/tex]
