Answer :
Let's examine each option to determine which ones correctly solve the equations provided:
1. Option A: [tex]\( x + 5 = 7 \)[/tex]; Solve for [tex]\( x \)[/tex]
- Start by isolating [tex]\( x \)[/tex] on one side of the equation:
[tex]\[
x + 5 = 7
\][/tex]
- Subtract 5 from both sides:
[tex]\[
x = 7 - 5
\][/tex]
- Calculate:
[tex]\[
x = 2
\][/tex]
- Therefore, the solution [tex]\( x = 2 \)[/tex] is correct for this equation.
2. Option B: [tex]\( x + 7 = 5 \)[/tex]; Solve for [tex]\( x \)[/tex]
- Isolate [tex]\( x \)[/tex] by subtracting 7 from both sides of the equation:
[tex]\[
x + 7 = 5
\][/tex]
- Subtract 7:
[tex]\[
x = 5 - 7
\][/tex]
- Calculate:
[tex]\[
x = -2
\][/tex]
- Thus, the solution [tex]\( x = -2 \)[/tex] is correct for this equation.
3. Option C: [tex]\( x = 5 + 7 \)[/tex]; Solve for [tex]\( x \)[/tex]
- Simply add the numbers on the right side:
[tex]\[
x = 5 + 7
\][/tex]
- Calculate:
[tex]\[
x = 12
\][/tex]
- Therefore, the solution [tex]\( x = 12 \)[/tex] is correct.
4. Option D: [tex]\( x + 7 = 12 \)[/tex]; Solve for [tex]\( x \)[/tex]
- To solve for [tex]\( x \)[/tex], subtract 7 from both sides:
[tex]\[
x + 7 = 12
\][/tex]
- Subtract 7:
[tex]\[
x = 12 - 7
\][/tex]
- Calculate:
[tex]\[
x = 5
\][/tex]
- Thus, the solution [tex]\( x = 5 \)[/tex] is correct for this equation.
So, each option given has a matching solution that correctly solves the associated linear equation.
1. Option A: [tex]\( x + 5 = 7 \)[/tex]; Solve for [tex]\( x \)[/tex]
- Start by isolating [tex]\( x \)[/tex] on one side of the equation:
[tex]\[
x + 5 = 7
\][/tex]
- Subtract 5 from both sides:
[tex]\[
x = 7 - 5
\][/tex]
- Calculate:
[tex]\[
x = 2
\][/tex]
- Therefore, the solution [tex]\( x = 2 \)[/tex] is correct for this equation.
2. Option B: [tex]\( x + 7 = 5 \)[/tex]; Solve for [tex]\( x \)[/tex]
- Isolate [tex]\( x \)[/tex] by subtracting 7 from both sides of the equation:
[tex]\[
x + 7 = 5
\][/tex]
- Subtract 7:
[tex]\[
x = 5 - 7
\][/tex]
- Calculate:
[tex]\[
x = -2
\][/tex]
- Thus, the solution [tex]\( x = -2 \)[/tex] is correct for this equation.
3. Option C: [tex]\( x = 5 + 7 \)[/tex]; Solve for [tex]\( x \)[/tex]
- Simply add the numbers on the right side:
[tex]\[
x = 5 + 7
\][/tex]
- Calculate:
[tex]\[
x = 12
\][/tex]
- Therefore, the solution [tex]\( x = 12 \)[/tex] is correct.
4. Option D: [tex]\( x + 7 = 12 \)[/tex]; Solve for [tex]\( x \)[/tex]
- To solve for [tex]\( x \)[/tex], subtract 7 from both sides:
[tex]\[
x + 7 = 12
\][/tex]
- Subtract 7:
[tex]\[
x = 12 - 7
\][/tex]
- Calculate:
[tex]\[
x = 5
\][/tex]
- Thus, the solution [tex]\( x = 5 \)[/tex] is correct for this equation.
So, each option given has a matching solution that correctly solves the associated linear equation.