Answer :
Let's solve this problem step by step to find the correct linear equation and its solution. The question provides four choices and we are looking to identify which equation is correct:
1. Choice 1: [tex]\(x + 7 = 5 \)[/tex] and the solution is [tex]\(x = -2\)[/tex].
2. Choice 2: [tex]\(x + 7 = 12 \)[/tex] and the solution is [tex]\(x = 5\)[/tex].
3. Choice 3: [tex]\(x + 5 = 7 \)[/tex] and the solution is [tex]\(x = 2\)[/tex].
4. Choice 4: [tex]\(x = 5 + 7\)[/tex] and the solution is [tex]\(x = 12\)[/tex].
Let’s check each equation to see which one is correctly solved:
Choice 1:
- Equation: [tex]\(x + 7 = 5\)[/tex]
- Solve for [tex]\(x\)[/tex]: Subtract 7 from both sides to isolate [tex]\(x\)[/tex].
[tex]\[
x + 7 - 7 = 5 - 7 \implies x = -2
\][/tex]
- The provided solution [tex]\(x = -2\)[/tex] is correct.
Choice 2:
- Equation: [tex]\(x + 7 = 12\)[/tex]
- Solve for [tex]\(x\)[/tex]: Subtract 7 from both sides to isolate [tex]\(x\)[/tex].
[tex]\[
x + 7 - 7 = 12 - 7 \implies x = 5
\][/tex]
- The provided solution [tex]\(x = 5\)[/tex] is correct.
Choice 3:
- Equation: [tex]\(x + 5 = 7\)[/tex]
- Solve for [tex]\(x\)[/tex]: Subtract 5 from both sides to isolate [tex]\(x\)[/tex].
[tex]\[
x + 5 - 5 = 7 - 5 \implies x = 2
\][/tex]
- The provided solution [tex]\(x = 2\)[/tex] is correct.
Choice 4:
- Equation: [tex]\(x = 5 + 7\)[/tex]
- Solve for [tex]\(x\)[/tex]: Perform the addition on the right side.
[tex]\[
x = 12
\][/tex]
- The provided solution [tex]\(x = 12\)[/tex] is correct.
Among all these choices, we see that choices 1, 2, 3, and 4 all have correct solutions with respect to their equations. However, based on a logical interpretation of the question as a balanced beam model, the primary correct choice appears to be Choice 1: [tex]\(x + 7 = 5\)[/tex] with [tex]\(x = -2\)[/tex], leading us to that particular result.
1. Choice 1: [tex]\(x + 7 = 5 \)[/tex] and the solution is [tex]\(x = -2\)[/tex].
2. Choice 2: [tex]\(x + 7 = 12 \)[/tex] and the solution is [tex]\(x = 5\)[/tex].
3. Choice 3: [tex]\(x + 5 = 7 \)[/tex] and the solution is [tex]\(x = 2\)[/tex].
4. Choice 4: [tex]\(x = 5 + 7\)[/tex] and the solution is [tex]\(x = 12\)[/tex].
Let’s check each equation to see which one is correctly solved:
Choice 1:
- Equation: [tex]\(x + 7 = 5\)[/tex]
- Solve for [tex]\(x\)[/tex]: Subtract 7 from both sides to isolate [tex]\(x\)[/tex].
[tex]\[
x + 7 - 7 = 5 - 7 \implies x = -2
\][/tex]
- The provided solution [tex]\(x = -2\)[/tex] is correct.
Choice 2:
- Equation: [tex]\(x + 7 = 12\)[/tex]
- Solve for [tex]\(x\)[/tex]: Subtract 7 from both sides to isolate [tex]\(x\)[/tex].
[tex]\[
x + 7 - 7 = 12 - 7 \implies x = 5
\][/tex]
- The provided solution [tex]\(x = 5\)[/tex] is correct.
Choice 3:
- Equation: [tex]\(x + 5 = 7\)[/tex]
- Solve for [tex]\(x\)[/tex]: Subtract 5 from both sides to isolate [tex]\(x\)[/tex].
[tex]\[
x + 5 - 5 = 7 - 5 \implies x = 2
\][/tex]
- The provided solution [tex]\(x = 2\)[/tex] is correct.
Choice 4:
- Equation: [tex]\(x = 5 + 7\)[/tex]
- Solve for [tex]\(x\)[/tex]: Perform the addition on the right side.
[tex]\[
x = 12
\][/tex]
- The provided solution [tex]\(x = 12\)[/tex] is correct.
Among all these choices, we see that choices 1, 2, 3, and 4 all have correct solutions with respect to their equations. However, based on a logical interpretation of the question as a balanced beam model, the primary correct choice appears to be Choice 1: [tex]\(x + 7 = 5\)[/tex] with [tex]\(x = -2\)[/tex], leading us to that particular result.
