| 4x- 2 |=24,5

The equation provided involves an absolute value. When solving an equation with absolute values, you need to consider both the positive and negative outcomes of the expression inside the absolute value. The equation is:

| 4x - 2 | = 24.5

This splits into two separate equations:

1. The positive case: 4x - 2 = 24.5

2. The negative case: 4x - 2 = -24.5

Let's solve for x in both cases:

1. Positive case: 4x - 2 = 24.5 Add 2 to both sides of the equation: 4x = 24.5 + 2 4x = 26.5 Now divide both sides by 4: x = 26.5 / 4 x = 6.625

2. Negative case: 4x - 2 = -24.5 Add 2 to both sides of the equation: 4x = -24.5 + 2 4x = -22.5 Now divide both sides by 4: x = -22.5 / 4 x = -5.625

So the solutions to the equation | 4x - 2 | = 24.5 are:

x = 6.625 and x = -5.625