`x+2 = 5` and `3x-1=8` have the same solutions.

Answer

To determine if the equations \( x + 2 = 5 \) and \( 3x - 1 = 8 \) have the same solutions, we will solve each equation step by step.

### Step 1: Solve the first equation \( x + 2 = 5 \)

1. Start with the equation:
\[ x + 2 = 5 \]

2. To isolate \( x \), subtract 2 from both sides:
\[ x + 2 - 2 = 5 - 2 \]
Simplifying this gives:
\[ x = 3 \]

### Step 2: Solve the second equation \( 3x - 1 = 8 \)

1. Start with the equation:
\[ 3x - 1 = 8 \]

2. To isolate the term with \( x \), add 1 to both sides:
\[ 3x - 1 + 1 = 8 + 1 \]
Simplifying this gives:
\[ 3x = 9 \]

3. Now, divide both sides by 3 to solve for \( x \):
\[ \frac{3x}{3} = \frac{9}{3} \]
Simplifying this gives:
\[ x = 3 \]

### Conclusion

Both equations yield the same solution:
\[ x = 3 \]

Therefore, the statement that \( x + 2 = 5 \) and \( 3x - 1 = 8 \) have the same solutions is correct.

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