Answer :
To solve the problem, we need to identify which of the given linear equations matches the solution, and then verify the solution by solving the equation.
Let's go through each option step-by-step:
1. Option 1: [tex]$x = 5 + 7 ; x = 12$[/tex]
- If we calculate the right-hand side, we have [tex]$x = 12$[/tex].
- The equation is stating that [tex]$x$[/tex] is directly 12, which confirms [tex]$x = 12$[/tex].
2. Option 2: [tex]$x + 7 = 5 ; x = -2$[/tex]
- To solve [tex]$x + 7 = 5$[/tex], subtract 7 from both sides:
[tex]\[
x + 7 - 7 = 5 - 7 \\
x = -2
\][/tex]
- This matches the given solution [tex]$x = -2$[/tex].
3. Option 3: [tex]$x + 5 = 7 ; x = 2$[/tex]
- To solve [tex]$x + 5 = 7$[/tex], subtract 5 from both sides:
[tex]\[
x + 5 - 5 = 7 - 5 \\
x = 2
\][/tex]
- This matches the given solution [tex]$x = 2$[/tex].
4. Option 4: [tex]$x + 7 = 12 ; x = 5$[/tex]
- To solve [tex]$x + 7 = 12$[/tex], subtract 7 from both sides:
[tex]\[
x + 7 - 7 = 12 - 7 \\
x = 5
\][/tex]
- This matches the given solution [tex]$x = 5$[/tex].
After evaluating all options, the equation and solution that correctly match what the problem statement indicates is:
[tex]\[x + 7 = 12 ; x = 5\][/tex]
Therefore, the correct answer is the one from option 4: [tex]\(x + 7 = 12\)[/tex] with the solution [tex]\(x = 5\)[/tex].
Let's go through each option step-by-step:
1. Option 1: [tex]$x = 5 + 7 ; x = 12$[/tex]
- If we calculate the right-hand side, we have [tex]$x = 12$[/tex].
- The equation is stating that [tex]$x$[/tex] is directly 12, which confirms [tex]$x = 12$[/tex].
2. Option 2: [tex]$x + 7 = 5 ; x = -2$[/tex]
- To solve [tex]$x + 7 = 5$[/tex], subtract 7 from both sides:
[tex]\[
x + 7 - 7 = 5 - 7 \\
x = -2
\][/tex]
- This matches the given solution [tex]$x = -2$[/tex].
3. Option 3: [tex]$x + 5 = 7 ; x = 2$[/tex]
- To solve [tex]$x + 5 = 7$[/tex], subtract 5 from both sides:
[tex]\[
x + 5 - 5 = 7 - 5 \\
x = 2
\][/tex]
- This matches the given solution [tex]$x = 2$[/tex].
4. Option 4: [tex]$x + 7 = 12 ; x = 5$[/tex]
- To solve [tex]$x + 7 = 12$[/tex], subtract 7 from both sides:
[tex]\[
x + 7 - 7 = 12 - 7 \\
x = 5
\][/tex]
- This matches the given solution [tex]$x = 5$[/tex].
After evaluating all options, the equation and solution that correctly match what the problem statement indicates is:
[tex]\[x + 7 = 12 ; x = 5\][/tex]
Therefore, the correct answer is the one from option 4: [tex]\(x + 7 = 12\)[/tex] with the solution [tex]\(x = 5\)[/tex].
