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.