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\[\left| x+1 \right|-3<4\]
My answer was x>6
I'm sorry, it was x<7
This is not an equation. It's an inequality The first step is to add 3 to both sides |dw:1441587163774:dw|
so we're left with `|x+1| < 7`
now you'll use the rule If \(\Large |x| < k\) then \(\Large -k < x < k\) where k is a positive number
so in this case, that rule makes `|x+1| < 7` turn into `-7 < x+1 < 7`
whats our next step?
next we subtract 1 from all sides to fully isolate x |dw:1441587398846:dw|
the '1's in the middle cancel since they add to 0 |dw:1441587429310:dw|
-7 - 1 is not equal to -6
on a number line would that look like this?
The draw function isnt working for me v.v
there would be an open circle at six and the arrow would go to the left continuously?
-7 - 1 = -8 instead think of it as "you're seven dollars in debt. You buy something worth 1 dollar. So you're now 8 dollars in debt"
Or would it stop at 8?
`-7 < x+1 < 7` becomes `-8 < x < 6`
here's what `-8 < x < 6` looks like |dw:1441587737649:dw| open circle at -8 open circle at 6 shading in between the open circles (do NOT fill in the open circles)