Question

Did I do it right this time?
|3-4x|≥7
|-4x+3|≥7
-7≤-4x+3≤7
-10≤-4x≤4
10/4≤x≤-1
final answer: (10/4, -1)

Answer 1

dang interval wrong again

Answer 2

gyaaah! darn

Answer 3

i think i confused you when i said to switch, so maybe it is better if you do not

Answer 4

ok, so then do I need to switch 10/4 and -1? or is it something else?

Answer 5

first of all you have an inequality that looks like this:
\[|\text{something}|>p\]

Answer 6

if you see this symbol
\[| blah| > p\] you should know that your answer will be TWO intervals, not one

Answer 7

if you have
\[|blah|<p\] one interval
\[|blah|> p\] TWO intervals

Answer 8

less than, one interval. greater than, two intervals. i know i am repeating myself but if you know this in advance it will make your live easier, trust me

Answer 9

so once you see
\[|3-4x|\geq7\] you should right away think "i am going to solve
TWO inequalities and get TWO intervals"

Answer 10

the two inequalities you have so solve are
\[3-4x\geq 7\] or
\[3-4x\leq -7\] and you have to solve them separately.

Answer 11

first one is
\[3-4x\geq 7\]
\[-4x\geq 4\]
\[x\leq -1\] note the change in sign when dividing by -4

Answer 12

second one is
\[3-4x\leq -7\]
\[-4x\leq -10\]
\[x\geq \frac{5}{2}\]

Answer 13

I forgot to simplify, didn't I?

Answer 14

and so your answer has two, count them, two intervals, they are
\[x\leq -1\] or
\[(-\infty,-1)\] or
\[x\geq \frac{5}{2}\] or
\[(\frac{5}{2},\infty)\]

Answer 15

yes but you also had one interval when you needed two intervals

Answer 16

that to
what is the purpose of the infinite?

Answer 17

you can write
\[(-\infty,-1)\cup (\frac{5}{2},\infty)\] if you like

Answer 18

how do you write
\[x\leq 1\] in interval notation?

Answer 19

it means x can be any number that is less than one. anything.

Answer 20

Ohhh ok. That makes sense. Thank you again!

Answer 21

yw. and don't forget please:
absolute value is LESS THAN gives ONE INTERVAL
absolute value GREATER THAN gives TWO INTERVALS

Answer 22

Wait, what is the U symbol?
and I wont!

Answer 23

that means "union" so it could be in one set OR the other

Answer 24

ok thanks!

Answer 25

you could just write the word OR instead

Answer 26

try another one carefully and see if you get it right. your algebra is correct, intervals are a problem

Answer 27

shouldnt we be using "[", "]" instead of "(",")" (on this side of the numbers in each interval - not for infinity) since we have "<=" and ">=" here ?

Answer 28

i.e.:
\[(-\infty,-1]\cup[\frac{5}{2},\infty)\]

Answer 29

yes of course you are right. i totally ignored that party. sorry. so much to think about...