50 POINTS FIRST GOOD ANSWER GETS BRAINLIEST Express f(x)=3+|2x-5| as a piecewise function WITHOUT using absolute value
Please give a detailed response not just answer to help me understand

Step-by-step explanation:

We are given the function:

Remember that by the definition of absolute value:

Our absolute value is:

First, we will find when it becomes 0. Set the equation equal to 0:

Solve for x:

So, we can see that for all values greater than x = 5/2, 2x - 5 is positive.

For all values less than x = 5/2, 2x - 5 is negative.

Therefore (the positive case go above, and the negative case go below):

Finally, we can add a three:

Simplify if desired: