Question

Solve each equation or inequality. If there is no solution, write no solution.
50. |n + 2| = 4

52. |x + 3| = -2

56. 4 |k + 5| > 8

Answer 1

hint: if u have |a|=b
the u can write
a=b OR a=-b

Answer 2

.........what

Answer 3

for example, if u have
|n + 2| = 4
you can write two equation and solve them individually,
n+2 =4 OR n+2 =-4
can u solve these equations ?

Answer 4

no I really don't understand this

Answer 5

which part ?
i think u can solve this to get n
n+2=4
n=?

Answer 6

2

Answer 7

correct!
now solve this to get other value of n
n+2=-4

Answer 8

-6

Answer 9

so the two values , u got for |n + 2| = 4 are n=2 or -6
got this ?

Answer 10

yeah but why is there two

Answer 11

is your question., why there are 2 solutions or is it why is n=2 ?

Answer 12

why are there two solutions?

Answer 13

because, for example |a| =4
u can put a =4 or a=-4
so most of the absolute value equations do have 2 solutions.
|....| makes the negative *minus* go away
hence, |-4| also equals 4.

Answer 14

ohhhhhhhhhhhhhhhhhh okay

Answer 15

AND |...| can never be a negative valued.
so what can u say about question 52. ?

Answer 16

-5?

Answer 17

|x + 3| = -2
but |..*anything*..| can never be negative.
so, |x+3| can never equal -2
hence, no solution, got this ?

Answer 18

because '|....| makes the negative *minus* go away'

Answer 19

ohh okay because since the | |'s make it not negative it wouldn't equal -2

Answer 20

yes, |x+3| will always be positive for ANY value of x.

Answer 21

try -5, |-5+3| = |-2| = ?

Answer 22

wait what? i'm confused again

Answer 23

as i said, |-a| = a
so |-2| = 2
hence its not -2 , just trying to explain, why -5 is not the solution....

Answer 24

ohhhhhhhh okay i didn't understand what you were asking. what about the last problem though? it's confusing because in the beginning there's a number and at the end instead of an equal sign there's a >

Answer 25

4 |k + 5| > 8
first isolate the absolute sign, by dividing by 4 ,what u get ?

Answer 26

what do i divide by 4? the 8?

Answer 27

both sides of the equation

Answer 28

so would the first 4 cancel out ? and then since id divide 4 and 8 it'd be 2?

Answer 29

thats correct.

Answer 30

so then it would be |k + 5| > 2??

Answer 31

yes.
now when |x|>a
means x>a and x<-a
so what about |k+5|>2 ?

Answer 32

k - 5 >2 ?

Answer 33

why k-5 ?

Answer 34

i meant + sorry

Answer 35

thats one eqution, solve it.

Answer 36

would it just be 5k? i dont get it

Answer 37

k+5 > 2
subtracting 5 from both sides
k+5-5 > 2-5
k> -3
got this ?

Answer 38

ohhh i didn't know i was supposed to subtract

Answer 39

since k was ADDED to 5 , to isolate k, we need to SUBTRACT 5.
now solve second equation k+5< -2

Answer 40

again by subtracting 5 from both sides

Answer 41

the answer would just be k> -3 then right? since that's what's left after you subtract the 5 from both sides?

Answer 42

k < -2-5
k< -7

Answer 43

OH

Answer 44

so after k> -2 you have to subtract 5 from the -2 again?

Answer 45

k>-2 is one solution to the original equation, now u also get
k< -7

Answer 46

so overall
-7 > k > -2

Answer 47

ohhh okay thanks

Answer 48

hope u understand a bit....
welcome :)

Answer 49

50. n = -6 and n = 2
52. False cannot be solved
56. Complicated, not sure I'd be able to explain it to you