Question

Equation A: -12+3x+2=x+2
Equation B: 8-3(x-1)=2
Equation C: -2+4x=10

Do any of these equations have the same answer?

Answer 1

To find out if any of the equations have the same solution, let's solve each equation step by step.

**Equation A:**
\[
-12 + 3x + 2 = x + 2
\]
Combine like terms:
\[
3x - 10 = x + 2
\]
Subtract \(x\) from both sides:
\[
3x - x - 10 = 2
\]
This simplifies to:
\[
2x - 10 = 2
\]
Add 10 to both sides:
\[
2x = 12
\]
Divide by 2:
\[
x = 6
\]

**Equation B:**
\[
8 - 3(x - 1) = 2
\]
Distribute -3:
\[
8 - 3x + 3 = 2
\]
Combine like terms:
\[
11 - 3x = 2
\]
Subtract 11 from both sides:
\[
-3x = 2 - 11
\]
This simplifies to:
\[
-3x = -9
\]
Divide by -3:
\[
x = 3
\]

**Equation C:**
\[
-2 + 4x = 10
\]
Add 2 to both sides:
\[
4x = 12
\]
Divide by 4:
\[
x = 3
\]

Now, summarizing the solutions:
- Equation A has \(x = 6\)
- Equation B has \(x = 3\)
- Equation C has \(x = 3\)

Equations B and C have the same solution, which is \(x = 3\).

**Conclusion:** Equations B and C have the same answer (3).