Solve the equation `x+4=-2` and check the result.

Options

A. `6`
B. `-6`
C. `12`
D. `0`

Answer

To solve the equation \( x + 4 = -2 \) and check the result, we can follow these steps:

### Step 1: Write down the equation
The given equation is:
\[ x + 4 = -2 \]

### Step 2: Isolate the variable \( x \)
To isolate \( x \), we need to move the constant term (which is \( 4 \)) to the right side of the equation. We can do this by subtracting \( 4 \) from both sides:
\[ x + 4 - 4 = -2 - 4 \]
This simplifies to:
\[ x = -6 \]

### Step 3: Write down the solution
The solution to the equation is:
\[ x = -6 \]

### Step 4: Check the result
To verify our solution, we will substitute \( x = -6 \) back into the original equation and check if both sides are equal.

**Left Hand Side (LHS)**:
\[ LHS = x + 4 = -6 + 4 = -2 \]

**Right Hand Side (RHS)**:
\[ RHS = -2 \]

### Step 5: Compare LHS and RHS
Now we compare the LHS and RHS:
\[ LHS = -2 \quad \text{and} \quad RHS = -2 \]

Since both sides are equal, we can conclude that our solution is verified.

### Final Answer
The solution to the equation \( x + 4 = -2 \) is:
\[ x = -6 \]

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