Need help solving an Absolute value equation - Algebra II

Question

precal · Answer

$$9\left| 4x+2 \right|-5=85$$

precal · Answer

Can I distribute the 9 to 4x and 2?

precal · Answer

Teacher said I could not.  I think she is wrong

kainui · Answer

I think your teacher is wrong, here's a graphical proof: https://www.desmos.com/calculator/yq9o1xjruf

precal · Answer

ok what property do I use?

kainui · Answer

This fact:
$$|a*b|=|a|*|b|$$

precal · Answer

I know there is two solutions.  She showed the graph

precal · Answer

operation inside is addition not multiplication

kainui · Answer

Well what you're trying to do is distribute, which is multiplication. I'm suggesting you plug in $a=9$ and $b=4x+2$.

precal · Answer

She won't take that information.  We were only given the following properties

kainui · Answer

I'm not gonna chase this around too much, it's a fact that you can distribute it like that but if your teacher is saying "do this with such and such rules" then maybe you can't do it with the rules you're given; at least not in one single step perhaps.

precal · Answer

To solve $$\left| ax+b \right|=c$$ when $$c \ge 0$$, solve the related linear equations ax+b=c or ax+b=-c

misty1212 · Answer

HI!!

misty1212 · Answer

a) add 5
b) divide by 9
c) remove the absolute value, don';t forget the $+$ and $-$

precal · Answer

Thanks Misty

misty1212 · Answer

and yes, your teacher is wrong, not that you really want to distribute, but you can if you like (it is more work)