If `4x+2=4`, what is the value of `4x-6`?

Options

A. `-6`
B. `-4`
C. `4`
D. `8`

Answer

To solve the equation \(4x + 2 = 4\) and find the value of \(4x - 6\), we can follow these steps:

### Step 1: Solve for \(4x\)
Start with the equation:
\[ 4x + 2 = 4 \]
To isolate \(4x\), subtract \(2\) from both sides:
\[ 4x = 4 - 2 \]

### Step 2: Simplify the equation
Now simplify the right side:
\[ 4x = 2 \]

### Step 3: Find the value of \(x\)
To find \(x\), divide both sides by \(4\):
\[ x = \frac{2}{4} = \frac{1}{2} \]

### Step 4: Substitute \(x\) into \(4x - 6\)
Now that we have \(x = \frac{1}{2}\), we can substitute this value into the expression \(4x - 6\):
\[ 4x - 6 = 4\left(\frac{1}{2}\right) - 6 \]

### Step 5: Calculate \(4x\)
Calculate \(4 \times \frac{1}{2}\):
\[ 4 \times \frac{1}{2} = \frac{4}{2} = 2 \]

### Step 6: Complete the expression
Now substitute this back into the expression:
\[ 4x - 6 = 2 - 6 \]

### Step 7: Simplify the final result
Finally, simplify \(2 - 6\):
\[ 2 - 6 = -4 \]

Thus, the value of \(4x - 6\) is \(-4\).

### Final Answer:
\[ \text{The value of } 4x - 6 \text{ is } -4. \]

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