Did I do this right? |3-7x|

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 (:

anonymous · Answer

looks good to me!

anonymous · Answer

but the interval is wrong

myininaya · Answer

is -1>13/7?

anonymous · Answer

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

anonymous · Answer

what myininaya is getting at in her socratic style

myininaya · Answer

lol

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

myininaya · Answer

your inequality notation is correct
your interval notation is wrong

anonymous · Answer

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

anonymous · Answer

$$13/7>x>-1$$ is right

anonymous · Answer

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

anonymous · Answer

yay

anonymous · Answer

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

anonymous · Answer

meaning 
$$|3-7x|<10$$ is the same as 
$$|7x-3|<10$$

anonymous · Answer

ok

myininaya · Answer

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

anonymous · Answer

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

anonymous · Answer

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.

anonymous · Answer

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