I4x-4I=8x+16 (The 2 "I" are absolute signs)

[4x - 4] = 8x + 16.

There are 2 possible solutions:
4x - 4 = +- (8x + 16),

First Eq:
4x - 4 = +(8x + 16),
4x - 8x = 16 + 4,
-4x = 20,
x = -5.

2nd Eq:
4x - 4 = -(8x + 16),
4x - 4 = -8x - 16,
4x + 8x = -16 + 4,
12x = -12,
x = -1.

Check 1st Eq:
[4*-5 -4] = 8*-5 + 16,
[-24] = -24.
The above statement is NOT true:
[-24] = +24.
Therefore, -5 is NOT a solution.

Check 2nd Eq:
[4*-1 - 4] = 8*-1 + 16,
[-8] = 8. TRUE.

Solution:x = -1.

To solve the equation I4x - 4I = 8x + 16 (with the absolute value signs), we need to consider two cases:

Case 1: I4x - 4I is positive.
In this case, the absolute value of 4x - 4 is equal to 4x - 4 (since 4x - 4 is already positive). Thus, we can rewrite the equation as 4x - 4 = 8x + 16.

Case 2: I4x - 4I is negative.
In this case, the absolute value of 4x - 4 is equal to -(4x - 4). To simplify further, we rewrite it as -4x + 4. Thus, we can rewrite the equation as -4x + 4 = 8x + 16.

Let's solve both cases:

Case 1: 4x - 4 = 8x + 16
First, we need to isolate the x terms by moving the constant terms to the right side and the x terms to the left side. We do this by subtracting 8x from both sides and adding 4 to both sides:
4x - 8x = 16 + 4
-4x = 20
Next, divide both sides of the equation by -4 to solve for x:
x = 20 / -4
x = -5

Case 2: -4x + 4 = 8x + 16
Again, let's isolate the x terms by moving the constant terms to the right side and the x terms to the left side. We do this by subtracting 8x from both sides and subtracting 4 from both sides:
-4x - 8x = 16 - 4
-12x = 12
To solve for x, we need to divide both sides of the equation by -12:
x = 12 / -12
x = -1

Therefore, the equation I4x - 4I = 8x + 16 has two solutions: x = -5 and x = -1.