1)|5x- 2 |- 2 = 4 2) | 3 -7 7x | =-2

Let's solve each equation step by step.

1. Equation: \( |5x - 2| - 2 = 4 \)

First, isolate the absolute value:

\[ |5x - 2| - 2 = 4 \] \[ |5x - 2| = 6 \]

Now we need to consider the two cases for the absolute value:

Case 1: \(5x - 2 = 6\)

\[ 5x = 8 \] \[ x = \frac{8}{5} = 1.6 \]

Case 2: \(5x - 2 = -6\)

\[ 5x = -4 \] \[ x = -\frac{4}{5} = -0.8 \]

So the solutions for the first equation are:

\[ x = 1.6 \quad \text{and} \quad x = -0.8 \]

2. Equation: \( |3 - 7(7x)| = -2 \)

This equation involves the absolute value. By definition, the absolute value cannot be negative, i.e., \( |A| \geq 0 \) for any \( A \). Thus, the equation

\[ |3 - 7(7x)| = -2 \]

does not have any solutions, since the absolute value cannot equal a negative number.

So, the conclusion for the second equation is:

No solutions.

You have:

1. \( x = 1.6 \) and \( x = -0.8 \) for the first equation.
2. No solutions for the second equation.