If `(2)//(5)(5x)+2(x-1)=4(x+1)-2`, what is the value of x?

Options

A. `x=-2`
B. `x=2`
C. There is no value of x for which the equation is true
D. There are infinitely many values of x for which the equation is true

Answer

To solve the equation \( \frac{2}{5}(5x) + 2(x - 1) = 4(x + 1) - 2 \), we will simplify and solve for \( x \) step by step.

### Step 1: Simplify the left-hand side
Start with the left-hand side of the equation:
\[ \frac{2}{5}(5x) + 2(x - 1) \]
The term \( \frac{2}{5}(5x) \) simplifies to \( 2x \) because the \( 5 \) cancels out:
\[ 2x + 2(x - 1) \]
Now distribute \( 2 \) in \( 2(x - 1) \):
\[ 2x + 2x - 2 \]
Combine like terms:
\[ 4x - 2 \]

### Step 2: Simplify the right-hand side
Now, simplify the right-hand side:
\[ 4(x + 1) - 2 \]
Distributing \( 4 \) gives:
\[ 4x + 4 - 2 \]
Combine the constants:
\[ 4x + 2 \]

### Step 3: Set the simplified sides equal to each other
Now we have:
\[ 4x - 2 = 4x + 2 \]

### Step 4: Subtract \( 4x \) from both sides
Subtract \( 4x \) from both sides:
\[ -2 = 2 \]

### Step 5: Analyze the result
The equation \( -2 = 2 \) is not true, which indicates that there is no value of \( x \) that satisfies the original equation.

### Conclusion
Since we reached a contradiction, we conclude that there is no solution for \( x \).