Solve the Absolute Value Equation System: |x+4| = |2x+20| with x > -10

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

• Step 1: Consider the equation $|x+4| = |2x+20|$.
• Step 2: Break it down into two separate cases.

We'll address each case separately below:

Case 1: $x + 4 = 2x + 20$

Simplifying gives:

$x + 4 = 2x + 20$
$4 = 2x - x + 20$
$4 = x + 20$
Subtracting 20 from both sides, we get:
$x = 4 - 20$
$x = -16$.

Since $x > -10$ is required, $x = -16$ is not valid.

Case 2: $x + 4 = -(2x + 20)$

Simplifying gives:

$x + 4 = -2x - 20$
Add $2x$ to both sides:
$x + 2x + 4 = -20$
$3x + 4 = -20$
Subtract 4 from both sides:
$3x = -24$
Divide by 3:
$x = -8$.

Check: Since $-8 > -10$, this solution is valid.

Thus, the solution to the problem is $x = -8$.