Question

solve abs(x+2)<=8+abs(2x-4)

Answer 1

so always

Answer 2

statement is true for all x in the real numbers

Answer 3

how about solve analytically, please

Answer 4

hmmm
so let's check the vertices
you have 2 absolute values, so you have 2 vertices

what makes |x+2| to 0? well x = -2, one vertex
what makes |2x-4| to 0? well x = 2, 2nd vertex

so we end up with 3 intervals to values against

Answer 5

where's the 8?

Answer 6

\(\bf \textit{left side -, right side -}\\
-x-2 \le 8-2x+4\\
\textit{setting x = -3}\\
3-2 \le 8+6+4 \textit{ \# true, thus is an answer}\)

Answer 7

ohh, the 8 is a shift, but in the graph is not used, just the vertices is all I used and the graph the expression itself

Answer 8

i see what you're doing...

Answer 9

and doing the test for the the 2nd interval and 3rd interval
with - and +
and + and +
for the expressions, will yield all of them are true, thus are solutions