Question

which answer is a solution to the inequality 4+|t+2|<11
A. t<5 and t>9
B. t>5 or t<-9
C.-5 10 years ago

Answer 1

first thing you may want to do is isolate the absolute value function

Answer 2

how do i do that?

Answer 3

take 4 off both sides

Answer 4

ok

Answer 5

so it will look like this |t+2|<11??

Answer 6

you took 4 from th eleft side, you have to do that to both sides to not change the equation

Answer 7

|t+2|<7 like this?

Answer 8

yes,
The absolute value of something, here t+2, can be thought of as a distance from zero, and distance is a positive value weather you are at a - value or + value, the distance from 0 is positive

Answer 9

you have to think a bit differently weather the absolute value is greater or less than some value.

Here it is less than, the distance is less than 11 , starting at a point, you can move +11 or -11 and the distance from the start is still +11, that is the general idea of absolute value

Answer 10

I am sorry, remember you took the 4 off, it is 7 not 11.

so if it is a less than, you are stuck between moving +7 and moving - 7

\[-7 <t+2<+7\]

Answer 11

so t in that case is on the interval of -9 to +5 , -9<t<5

Answer 12

on the other hand if you simplify do isolate the absolute value, and you have that it is "Greater than " some value...

then the distance has to be "at least some number"

Answer 13

so the answer is C?

Answer 14

example, just change the sign to greater in the last prob

abs(t+2) > 11

here you get two seperated intervals, the distance is at least a certain amount, solve for both

t + 2 =11
or
t + 2 =-11

Answer 15

right, C

for the other sign, you get an OR instead of a compound AND inequality

Answer 16

t>9 or t<-13

Answer 17

a split interval...

here is a reference i found/
http://www.purplemath.com/modules/absineq.htm

Answer 18

Alright thank you :))

Answer 19

welcome

Answer 20

before you go can you check my answer on my last question please?

Answer 21

Select the graph that represents the solution of the open sentence.
3|p| – 5 < 7

Answer 22

k

Answer 23

isolate the absolute value first
add 5 both sides
divide by 3 both sides

abs(p) < 4

Answer 24

less than means the distance is at most 4 in either direction from where you start, zero

-4<p<4

good