Question

Did I do this right?
|3-7x|<10
-10<3-7x<10
-13<-7x<7
13/7>x>-1
final answer: (13/7, -1)
I'm not very good at math, so any help is much appreciated (:

Answer 1

looks good to me!

Answer 2

but the interval is wrong

Answer 3

is -1>13/7?

Answer 4

you have to put the smaller number on the left and the bigger one on the right

Answer 5

what myininaya is getting at in her socratic style

Answer 6

lol

Answer 7

in other words there is no such interval is
\[(5,-2)\] fro example you have to write
\[(-2,5)\]

Answer 8

So I'm not supposed to switch the signs when I divide?

Answer 9

you did that correctly, but it was unnecessary let me show you why

Answer 10

your inequality notation is correct
your interval notation is wrong

Answer 11

hold on a second. all your work is correct. the interval notation is wrong

Answer 12

\[13/7>x>-1\] is right

Answer 13

Ohhh, so instead its (-1, 13/7)?

Answer 14

yay

Answer 15

now let me show you why you do not need to worry about switching the inequality at your third step. convince yourself that
\[|a-b|=|b-a|\]

Answer 16

meaning
\[|3-7x|<10\] is the same as
\[|7x-3|<10\]

Answer 17

ok

Answer 18

|a-b|=|(-1)(-a+b)|=|-1|*|-a+b|=1*|b-a|=|b-a|

Answer 19

now solve as follows:
\[|7x-3|<10\]
\[-10<7x-3<10\]
\[-7<7x<13\]
\[-1<x<\frac{13}{7}\]

Answer 20

and now the order is preserved. you do need an additional step at the beginning so if this is confusing ignore me and solve as you are used to but make sure to write your solution correctly.

Answer 21

ok this makes sense. All I have to do is keep the variable in front?