solve `(x-6)+(x-4)=4`

Options

A. `sqrt2`
B. `7`
C. `14`
D. `2sqrt7`

Answer

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

### Step 1: Combine like terms
Start by combining the terms on the left side of the equation.

\[ (x - 6) + (x - 4) = 4 \]

This simplifies to:

\[ x + x - 6 - 4 = 4 \]

### Step 2: Simplify the equation
Combine the \(x\) terms and the constant terms:

\[ 2x - 10 = 4 \]

### Step 3: Isolate the variable
Next, we want to isolate \(2x\) by adding \(10\) to both sides of the equation:

\[ 2x - 10 + 10 = 4 + 10 \]

This simplifies to:

\[ 2x = 14 \]

### Step 4: Solve for \(x\)
Now, divide both sides by \(2\) to solve for \(x\):

\[ x = \frac{14}{2} \]

This gives us:

\[ x = 7 \]

### Final Answer
Thus, the solution to the equation \((x-6) + (x-4) = 4\) is:

\[ \boxed{7} \]

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