Question

Solve |2y+6|<10 for inequality and write the solution in interval notation and graph

Answer 1

(2y+6)<10 and -(2y+6)<10
2 y < 4 and -2y - 6 < 10
y < 2 and -y < 8 (which is y > -8)
looks like between -8 and +2
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check
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well try y = 0, yes |6| is <10
try y = -7, yes |-8| is <10
try y = +1, yes |+8| is <10

Answer 2

|2y+6|<10
2y+5 < 10 AND -2y-6 < 10
2y < 5 AND -2y < 16
y < 5/2 AND y > -8

in traditional notation: -8 < y < 5/2

I will let you express it in interval notation

your graph should consist of a line joining -8 to 5/2, with the end points
consisting of open circles.
that is, you want all the values between -8 and 5/2

Answer 3

argghhh, don't know how my 6 turned into a 5 in line 2

go with "anonymous"

Answer 4

|2y+6|<10
|y+3| < 5
(y+3)^2 < 5^2
y^2+6y+9 < 25
y^2+6y-16 < 0
(y-2)(y+8) < 0
solution interval: (-8,2)
graph is at
https://www.wolframalpha.com/input/?i=%7C2y%2B6%7C%3C10

or,
|2y+6| < 10
|y+3| < 5
so you want all the points within 5 of the value -3.
-3-5 < y < -3+5
-8 < y < 2