Question

How do i solve this .75x4 – 8 = -12

Answer 1

Assuming the .75x4 is .75 times x times for and not .75 times four...
Firstly, know you want x on its own.

So I’d start by adding 8 to both sides. This cancels out the -8:

.75x *4 - 8 = -12
+8 +8

= .75x * 4 = -4

Now divide by 4, both sides.
.75x * 4 = -4
———————
4

=.75x = -1

Finally, divide both sides by .75:

.75x = -1
—————
.75

= x = -1.33 (33 repeating) OR -4/3

But if you meant .75x^4 - 8 = -12 then here’s the answer.

First you add 8 to both sides, so:

75x^4 - 8 = -12
+8 +8

= .75x^4 = -4

Now divide both sides by .75:

.75x^4 = -4
——————
.75

= x^4 = -5.3333 OR -16/3

Now’s the harder part. We need to get rid of ^4 from x. Which means taking the root (both sides)...

An easier way to say this, and how I prefer to set it up, is + or - (-16/3)^(1/4)

You have the + or 1 part because the square root of something is always able to be positive or negative— as an easy example, 2*2=4 and -2*-2=4, so root of 4 could be -2 or 2. Anyways for this problem there aren’t any real solutions.

If your teacher is expecting you to use i in order to get the answers (for this last part, assuming they wanted .75x^4 and not .75x*4) then I can explain in the comments but it’s definitely harder than what I’ve shown here.