If `x + 3 = 4x + 4 and 3 (4-x) - 4 = 2z - 2,` then x can take which of the following values ?

Options

A. 1
B. 3
C. `-1`
D. `-3`

Answer

To solve the given equations step by step, we will first address the equation \( x + 3 = 4x + 4 \) and then the second equation \( 3(4 - x) - 4 = 2z - 2 \).

### Step 1: Solve the first equation \( x + 3 = 4x + 4 \)

1. Start by isolating \( x \) on one side of the equation.
\[ x + 3 = 4x + 4 \]

2. Subtract \( x \) from both sides:
\[ 3 = 4x - x + 4 \]
\[ 3 = 3x + 4 \]

3. Now, subtract 4 from both sides:
\[ 3 - 4 = 3x \]
\[ -1 = 3x \]

4. Finally, divide both sides by 3 to solve for \( x \):
\[ x = -\frac{1}{3} \]

### Step 2: Substitute \( x \) into the second equation \( 3(4 - x) - 4 = 2z - 2 \)

1. Substitute \( x = -\frac{1}{3} \) into the equation:
\[ 3\left(4 - \left(-\frac{1}{3}\right)\right) - 4 = 2z - 2 \]

2. Simplify the expression inside the parentheses:
\[ 4 + \frac{1}{3} = \frac{12}{3} + \frac{1}{3} = \frac{13}{3} \]

3. Now substitute this back into the equation:
\[ 3\left(\frac{13}{3}\right) - 4 = 2z - 2 \]

4. The \( 3 \) cancels with the denominator:
\[ 13 - 4 = 2z - 2 \]
\[ 9 = 2z - 2 \]

5. Add 2 to both sides:
\[ 9 + 2 = 2z \]
\[ 11 = 2z \]

6. Divide both sides by 2 to solve for \( z \):
\[ z = \frac{11}{2} \]

### Conclusion

The value of \( x \) that satisfies the first equation is:
\[ \boxed{-\frac{1}{3}} \]