Question

Solve the inequality. 4 + |t + 2| < 11

A.
t < 5 and t > 9

B.
t > 5 or t < –9

C.
–5 < t < 9

D.
–9 < t < 5

Answer 1

subtract 4 on both sides first

Answer 2

let a>0.

If you have |f(x)|<a => -a<f(x)<a
Example: |x-9|<4 => -4<x-9<4
If you have |f(x)|>a => f(x)>a or f(x)<-a
Example |x-9|>4 => f(x)>4 or f(x)<-4
Tell me which form do you have.

Answer 3

I don't really get it..

Answer 4

Try which one do you have
|f(x)|>a or |f(x)|<a ?

Answer 5

I hope you have already subtracted 4 on both sides

Answer 6

um I think it's f(x) >a..

Answer 7

4 + |t + 2| < 11
you have subtracted 4 on both sides
getting
|t+2|<11-4
|t+2|<7

so you think it looks like |f(t)|>7?

In your inequality the inequality is pointing the other way.

Answer 8

oh, sorry I thought I was supposed to change it

Answer 9

Use the formulas I gave.

Answer 10

If you have |f(t)|<a then -a<f(t)<a
If you have |f(t)|>a then f(t)>a or f(t)<-a
we have |t+2|<7
so again looking at the if..then statements our inequality satisfies the if part of the first sentence
so we will use the then part of that sentence to solve for t

Answer 11

so what does our then part look like

replace f(t) with t-2
and
replace a with 7

Answer 12

-7 < t-2 < -7 ?

Answer 13

not quite
we have |f(t)|<a which implies -a<f(t)<a
we have |t-2|<7 which implies -7<t-2<7




(also these definitions are only for a>0)

Answer 14

do you know how to solve -7<t-2<7 for t?

Answer 15

Your objective is to isolate t.
How do you undo that subtraction of 2 next to that t?

Answer 16

I think I know what it is '.'

Answer 17

what do you think it is?

Answer 18

I think i changed your t+2 to t-2
my bad
we have -7<t+2<7

Answer 19

ya I think it's C

Answer 20

Almost..

we have -7<t+2<7 not -7<t-2<7

Answer 21

Then would it be D?

Answer 22

yep

Answer 23

THANK YOU! :D

Answer 24

np

Answer 25

goof job