Answer:
[tex]x=\frac{85}{16}, x=-\frac{85}{16}[/tex]
Step-by-step explanation:
Hi there!
We are given the absolute value equation:
5-8|-2x|=-80
We want to solve it for x
First, let's make sure that ONLY the absolute value equation is on the left side
So subtract 5 from both sides
-8|-2x|=-85
Now divide both sides by -8
|-2x|=85/8
Now, for an absolute value equation, we can split it up into two parts, as |x| can be equal to both x and -x
In this case, |-2x| can equal to 85/8, but it can also equal -85/8
That's why for absolute value, there are always 2 cases
For the first case, if |-2x| is equal to 85/8:
Note: we open up the absolute value when we are solving a case, as it is one of the possiblities that can happen for the equation. So it would be true.
-2x=85/8
Divide both sides by -2
x=-85/16
In the second case, if -2x is equal to -85/8:
-2x=-85/8
Divide both sides by -2
x=85/16
So the answers are [tex]x=\frac{85}{16}, x=-\frac{85}{16}[/tex]
Hope this helps!
