Did i do this right??

[toastonrye]

this is part of a rational question, which the scenario is all negatives
| |x+2| +4| =10

-(-( x + 2 )+ 4) = 2
x+2-4=10
x-2=10
x=12 { }

no solution

??
thanks

 

[Unco]

\(\displaystyle \mbox{\left| x + 2 \right| + 4 > 0}\) for all \(\displaystyle \mbox{x}\) since \(\displaystyle \mbox{| x + 2 | \geq 0 }\) so the outermost absolute value signs in \(\displaystyle \mbox{\left| | x + 2 | + 4 \right| = 10 }\) are redundant.

So we have
\(\displaystyle \mbox{ |x+2| + 4 = 10 }\)

Now solve for x.