Question

|5x|+5=45 can you explain this absloute value equation i have a midterm

Answer 1

So first, you get the absolute value to one side:
$|5x|+5=45\\ |5x|=40$

Next, set up two equations; One where the value inside the absolute value lines is positive, and another where it is negative, and solve both for the variable:
$|5x|=40\\5x=40\\x=\frac{40}{5}=8\\\\-5x=40\\x=\frac{40}{-5}=-8$

Your answers are 8 and -8, or +-8.

Answer 2

In absolute value you always get 2 answer a positive and a negative
|5x|+5=45
+-5x=40
x=+-8