Question

Solve the inequality. 2 + |t + 6| < 12

Answer 1

Similar Problem (just with different numbers)


\[\Large 5 + |t + 3| < 27\]


\[\Large |t + 3| < 27-5\]


\[\Large |t + 3| < 22\]


\[\Large -22< t + 3 < 22\]


\[\Large -22-3 < t < 22-3\]


\[\Large -25 < t < 19\]

Answer 2

Again, keep in mind that is just a similar example

Answer 3

|t+6|=10

Answer 4

If |t+6|=10, then t+6 = 10 or t+6 = -10

solve each equation for t

Answer 5

-16<t<4?

Answer 6

t+6 = 10
t = ???

Answer 7

t=4 :)

Answer 8

t+6 = -10
t = ???

Answer 9

t=-16

Answer 10

So if |t+6|=10, then t = 4 or t = -16

Answer 11

I see.

Answer 12

A.


t > 4 or t < –11


B.


t < 4 and t > 11


C.


–16 < t < 4


D.


–4 < t < 16

Answer 13

So C is correct right?

Answer 14

there's a typo in |t+6|=10

Answer 15

that equal sign should be something else

Answer 16

Should be < right?

Answer 17

idk, i can't see your screen/paper

Answer 18

But C is supposed to be correct right?

Answer 19

The original problem has a typo in it. The equation just yields 2 solutions (not infinitely many)

Answer 20

Ok...

Answer 21

IF the original problem is |t+6|<10, then you'd be right

Answer 22

but the problem is |t+6|=10

Answer 23

Ok thanks for your help

Answer 24

you're welcome

Answer 25

@jim_thompson5910 .. this line

−22<t+3<22

−22−3<t<22−3

can you please explain mathematically what happens here?
as in, if there was a description- take 3 away from....

Answer 26

I'm subtracting 3 from ALL sides to isolate t

Answer 27

since in the middle +3 - 3 = 0, it goes away

but you must do the same to every side to balance things out

Answer 28

right, just like how we would solve a equation, balancing out :) thanx!

Answer 29

sure thing

Answer 30

@jim_thompson5910 one more question, might sound silly...would u call this an equation, even though there are 3 sides to it? or is there another mathematical term

Answer 31

This is NOT an equation because there are NO equal signs

This is an inequality (more specifically a compound inequality)

Answer 32

opps yes i was aware it is an inequality... but balancing the 3 side s like we do with equation and in equations.. thats why i asked if there was a specific name for it

Answer 33

i guess it is just an inequation simplified right.

Answer 34

When you solve an inequality, you follow the same basic steps as you would when solving equations. You need to maintain balance throughout all of the steps to make sure you don't change the original (so you can properly isolate the variable)

Answer 35

The key difference with inequalities is that the inequality sign will flip if you multiply/divide both sides by a negative number

Answer 36

ok, right. thanx for that i appreciate it

Answer 37

you're welcome