Solve the Absolute Value Equation: |x + 2| = 4

To solve this problem, we'll follow these steps:

• Step 1: Set up two linear equations from the absolute value definition.
• Step 2: Solve each equation for $x$.

Now, let's work through each step:

Step 1: Consider the two cases from $\left|x + 2\right| = 4$.

• First case: $x + 2 = 4$.
• Second case: $x + 2 = -4$.

Step 2: Solve the two equations:

For the first case:

$x + 2 = 4$

Subtract 2 from both sides:

$x = 4 - 2$ $x = 2$

For the second case:

$x + 2 = -4$

Subtract 2 from both sides:

$x = -4 - 2$ $x = -6$

Therefore, the solutions to the equation $\left|x + 2\right| = 4$ are:

$x = -6$ and $x = 2$.

The correct option is:

$x = -6, x = 2$

Thus, the solution to the problem is:

$x = -6, x = 2$