Hello, 4 little piggies mom!
Given: \(\displaystyle \;|x\,-\,7|\:=\:4\)
My son has \(\displaystyle |x|\,=\,11\)
I think that this should end up with : \(\displaystyle x=11\) or \(\displaystyle x=3\)
You're right, Mom!
\(\displaystyle |x\,-\,7|\,=\,4\) means
two equations:
. . . . . \(\displaystyle x\,-\,7\:=\:4\;\;\Rightarrow\;\;x\,=\,11\)
and: \(\displaystyle \;x\,-\,7\:=\:\)-\(\displaystyle 4\;\;\Rightarrow\;\;x\,=\,3\)
Often, we can think of an absolute value as a <u>distance</u>.
\(\displaystyle |x\,-\,7|\:=\:4\:\) means: the distance from \(\displaystyle x\) to \(\displaystyle "7"\) is 4 units.
. . That is, find \(\displaystyle x\) which is 4 units from "7".
And we find two values: one is 11, the other is 3.
