SOLUTION: I need the answers to these questions: |(2x+(1/3))x +0.3|=3.5 and |(-2x+(1/3))x+0.3|=3.5

Algebra ->  Absolute-value -> SOLUTION: I need the answers to these questions: |(2x+(1/3))x +0.3|=3.5 and |(-2x+(1/3))x+0.3|=3.5      Log On


   



Question 1020900: I need the answers to these questions:
|(2x+(1/3))x +0.3|=3.5
and
|(-2x+(1/3))x+0.3|=3.5

Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
They are somewhat alike, and if you understand how to handle either, you can handle the other.

abs%28%282x%2B%281%2F3%29%29x%2B0.3%29=3.5

Distribute.
abs%282x%5E2%2Bx%2F3%2B0.3%29=3.5
Maybe easier if clear the fractions denominators...
3%2Aabs%282x%5E2%2Bx%2F3%2B0.3%29=3%2A%283.5%29
abs%286x%5E2%2Bx%2B0.9%29=10.5, not perfectly, but good enough to continue comfortably.

Either the input to the absolute value is non-negative, or it is negative. Solve for each of these two cases.


NON-NEGATIVE
6x%5E2%2Bx%2B0.9=10.5
6x%5E2%2Bx%2B0.9-10.5=0
6x%5E2%2Bx-9.6=0
Discrim is 1%2B4%2A6%2A9.6=231.4

NEGATIVE
-6x%5E2-x-0.9=10.5
6x%5E2%2Bx%2B0.9=-10.5
6x%5E2%2Bx%2B0.9%2B10.5=0
6x%5E2%2Bx%2B11.4=0
Discrim is 1-4%2A6%2A11.4=negativeValueDiscriminant
These will not be real numbers.

Continue for the non-negative inputs to the absolute value.
highlight%28x=%28-1%2B-+sqrt%28231.4%29%29%2F12%29

You may want to check both values in case one of them does not work in the original equation.