| 4x- 2 |=24,5

To solve the absolute value equation |4x - 2| = 24.5, we need to consider the two cases that arise from the definition of the absolute value function. The absolute value of a number is the distance of that number from 0 on the real number line without consideration to direction, meaning:

1. The expression inside the absolute value sign is equal to 24.5.
2. The expression inside the absolute value sign is equal to -24.5.

Thus, we have two separate equations to solve:

Case 1: 4x - 2 = 24.5 Add 2 to both sides: 4x = 24.5 + 2 4x = 26.5 Now divide by 4: x = 26.5 / 4 x = 6.625

Case 2: 4x - 2 = -24.5 Add 2 to both sides: 4x = -24.5 + 2 4x = -22.5 Now divide by 4: x = -22.5 / 4 x = -5.625

Therefore, the two solutions to the equation |4x - 2| = 24.5 are x = 6.625 and x = -5.625.