Question

i am not sure how to solve this inequality. can you please show me how to do it?

2|x+1/3|<9

Answer 1

so basically when dealing with absolute values, you're going to have two solution set
when x is less than or equal to zero, and when x is greater than zero

4| x + 2/5| < 20 becomes

4* -1(x + 2/5) < 20
and
4 * 1(x + 2/5) < 20

solve for both x's and the answer should be the interval of your x

Answer 2

how did you get 20 in the beginning?

Answer 3

in the first one,
4 * (-x - 2/5) < 20
-4x -8/5 <20
-4x < 20 + 8/5
-4x < 100/5 + 8/5
-4x < 108/5
x > -108/20
the sign < flips to > because our -x was divided by -1 (this is always the case.)

for the second one

4 * (x + 2/5) < 20
4x + 8/5 < 20
4x < 20 - 8/5
4x < 100/5 - 8/5
4x < 92/5
x < 92/20

Answer 4

it is a different set of problem but using the same concept

Answer 5

ohh ok give me a sec to try it out

Answer 6

okay

Answer 7

2|x+1/3|<9
-2x-4/3<9
-2x<9+4/3
im stuck here..i know you made the 20 go 5 times in 100 but i dont know what to do with the numbers i have

Answer 8

@nincompoop

Answer 9

how did you get -4/3?
it is 2 * -1(x + 1/3) < 9 right?
use distributive property -1 * (x + 1/3) first
that's (-x -1/3)
then multiply by 2
2 (-x -1/3 )
-2x -2/3

Answer 10

so that's
-2x - 2/3 < 9
now leave -2x on the left side by itself by adding 2/3 on both sides of the inequality
-2x -2/3 + 2/3 < 9 + 2/3

Answer 11

oh i mustve mixed up your example with my equation..
so then its -2x<9+2/3

Answer 12

what fraction do i turn the 9 into?

Answer 13

try multiplying it by 3
(9*3)/3 is like multiplying 9 * 3/3
3/3 is 1 so you're not actually changing the value, you're just making it similar to the denominator of the other fraction so you don't have to look for the LCD later on

Answer 14

-2x<27/3+2/3
-2x<29/3

Answer 15

good
now solve for x by dividing both sides by -2

Answer 16

how is 29/3 dividable by 2??

Answer 17

29/3/2 is the same as
29/3 ÷ 2/1 correct?
so when dividing two fractions
you obtain the reciprocal of the other and then multiply
2/3 * 1/2 = ?

Answer 18

in your case it is 29/3 * 1/2

Answer 19

so thats 29/6? or is it 29/3*2/1 (the reciprocal)?

Answer 20

29/6