| 4x- 2 |=24,5

The absolute value equation | 4x - 2 | = 24.5 can be solved by considering the definition of the absolute value function. This function outputs the distance of a number from zero on the number line, so it is always non-negative.

Since the absolute value of an expression can yield the same number whether the expression inside is positive or negative, we have two cases to consider:

Case 1: The expression inside the absolute value is positive or zero, so we can simply remove the absolute value bars:

4x - 2 = 24.5

Now, solve for x:

4x = 24.5 + 2 4x = 26.5 x = 26.5 / 4 x = 6.625

Case 2: The expression inside the absolute value is negative, so the output is the positive equivalent. In such a case, we consider the negative of the expression inside and set it equal to 24.5:

-(4x - 2) = 24.5 -4x + 2 = 24.5

Now, solve for x:

-4x = 24.5 - 2 -4x = 22.5 x = 22.5 / -4 x = -5.625

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

x = 6.625 or x = -5.625