For which equation(s) is x= 3 a solution?
(I) `2x - 5 + 3x = 10` (II) `(-x + 7)/(2) = 2`
(III) `4x - 11 = 17`  (IV) `9 = -(x-1) + 11`

Options

A. I only
B. I and II
C. I, II and III
D. I, II and IV

Answer

To determine for which equations \( x = 3 \) is a solution, we will substitute \( x = 3 \) into each equation and check if the equation holds true.

### Step-by-step Solution:

**Equation (I):** \( 2x - 5 + 3x = 10 \)

1. Substitute \( x = 3 \):
\[ 2(3) - 5 + 3(3) = 10 \]
2. Calculate:
\[ 6 - 5 + 9 = 10 \]
3. Simplify:
\[ 10 = 10 \quad \text{(True)} \]

**Conclusion:** \( x = 3 \) is a solution for Equation (I).

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**Equation (II):** \( \frac{-x + 7}{2} = 2 \)

1. Substitute \( x = 3 \):
\[ \frac{-3 + 7}{2} = 2 \]
2. Calculate:
\[ \frac{4}{2} = 2 \]
3. Simplify:
\[ 2 = 2 \quad \text{(True)} \]

**Conclusion:** \( x = 3 \) is a solution for Equation (II).

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**Equation (III):** \( 4x - 11 = 17 \)

1. Substitute \( x = 3 \):
\[ 4(3) - 11 = 17 \]
2. Calculate:
\[ 12 - 11 = 17 \]
3. Simplify:
\[ 1 = 17 \quad \text{(False)} \]

**Conclusion:** \( x = 3 \) is NOT a solution for Equation (III).

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**Equation (IV):** \( 9 = -(x - 1) + 11 \)

1. Substitute \( x = 3 \):
\[ 9 = -(3 - 1) + 11 \]
2. Calculate:
\[ 9 = -2 + 11 \]
3. Simplify:
\[ 9 = 9 \quad \text{(True)} \]

**Conclusion:** \( x = 3 \) is a solution for Equation (IV).

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### Final Summary:
The equations for which \( x = 3 \) is a solution are:
- Equation (I)
- Equation (II)
- Equation (IV)