Question

5-8|-2x|=-80 Blank 1: ? Blank 2: ?

Answer 1

Answer:

$x=\frac{85}{16}, x=-\frac{85}{16}$

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 $x=\frac{85}{16}, x=-\frac{85}{16}$

Hope this helps!