Solve the following equations and verify the results.
`5x -2 = 3x - 4`

Options

A. x = - 2
B. x = - 3
C. x = - 1
D. x = - 4

Answer

To solve the equation \(5x - 2 = 3x - 4\) step by step, follow these instructions:

### Step 1: Start with the given equation
\[ 5x - 2 = 3x - 4 \]

### Step 2: Move all terms involving \(x\) to one side
Subtract \(3x\) from both sides:
\[ 5x - 3x - 2 = -4 \]
This simplifies to:
\[ 2x - 2 = -4 \]

### Step 3: Move the constant term to the other side
Add \(2\) to both sides:
\[ 2x - 2 + 2 = -4 + 2 \]
This simplifies to:
\[ 2x = -2 \]

### Step 4: Solve for \(x\)
Divide both sides by \(2\):
\[ x = \frac{-2}{2} \]
This simplifies to:
\[ x = -1 \]

### Step 5: Verification
To verify, substitute \(x = -1\) back into the original equation:
\[ 5(-1) - 2 = 3(-1) - 4 \]
Calculating both sides:
Left-hand side:
\[ 5(-1) - 2 = -5 - 2 = -7 \]
Right-hand side:
\[ 3(-1) - 4 = -3 - 4 = -7 \]
Since both sides are equal:
\[ -7 = -7 \]
This confirms our solution.

### Final Solution
Thus, the solution to the equation \(5x - 2 = 3x - 4\) is:
\[ x = -1 \]