To solve the problem of selecting the correct linear equation and solving it, we need to follow a step-by-step method. Let’s carefully analyze each of the given options within the context of solving for [tex]\( x \)[/tex].
1. Option 1: [tex]\( x + 5 = 7 ; x = 2 \)[/tex]
- Solve the equation [tex]\( x + 5 = 7 \)[/tex]:
[tex]\[ x + 5 = 7 \][/tex]
Subtract 5 from both sides:
[tex]\[ x = 7 - 5 \][/tex]
[tex]\[ x = 2 \][/tex]
- Result: [tex]\( x = 2 \)[/tex]
- This is a valid equation, but let’s analyze the other options for completeness.
2. Option 2: [tex]\( x + 7 = 12 ; x = 5 \)[/tex]
- Solve the equation [tex]\( x + 7 = 12 \)[/tex]:
[tex]\[ x + 7 = 12 \][/tex]
Subtract 7 from both sides:
[tex]\[ x = 12 - 7 \][/tex]
[tex]\[ x = 5 \][/tex]
- Result: [tex]\( x = 5 \)[/tex]
3. Option 3: [tex]\( x + 7 = 5 ; x = -2 \)[/tex]
- Solve the equation [tex]\( x + 7 = 5 \)[/tex]:
[tex]\[ x + 7 = 5 \][/tex]
Subtract 7 from both sides:
[tex]\[ x = 5 - 7 \][/tex]
[tex]\[ x = -2 \][/tex]
- Result: [tex]\( x = -2 \)[/tex]
4. Option 4: [tex]\( x = 5 + 7 ; x = 12 \)[/tex]
- Solve the equation [tex]\( x = 5 + 7 \)[/tex]:
[tex]\[ x = 5 + 7 \][/tex]
[tex]\[ x = 12 \][/tex]
- Result: [tex]\( x = 12 \)[/tex]
- Note: This option does not follow the standard form of a linear equation with a balance point but let’s verify the given answer.
Given the correct and final value seen in the solved problem, the equation should provide a result where [tex]\( x = 5 \)[/tex].
Thus, among the provided options, the correct equation is:
[tex]\( x + 7 = 12; x = 5 \)[/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{x + 7 = 12; x = 5} \][/tex]
