Question

Can someone explain to me how to solve this ?

Answer 1

\[2 - 3 \left| x \right| > \left| x \right| - 10\]

Answer 2

2+ 10 > |x| + 3|x|
|x| < 3

Answer 3

I don't understand what you did after 2+ 10 > |x| + 3|x|

Answer 4

2+ 10 > |x| + 3|x|

2+10 is 12, and 1 |x| plus 3 more |x| is 4 |x|

12 > 4|x|

divide both sides by 4
3 > |x|
this means 3 > x and 3 > -x
3 > -x can be re-arranged: add +x to both sides to get
3 + x > 0
add -3 to both sides to get
x > -3

you have
3 > x and x> -3
which can be written as
-3 < x and x < 3 or -3 < x < 3

Answer 5

Thanks a lot @phi !!!! Do you mind telling me how the graph of this inequality would look like? If you don't mind

Answer 6

people also use a "rule" : if you multiply both sides by -1, "flip" the relation so
3 > -x
becomes
-3 < x

but if you only add, you don't have to remember this rule

Answer 7

The graph will be a number line, and it will show which x values are "allowed"

in other words, the graph will show -3 < x < 3
which, in English, means x is bigger than -3 and less than +3
x does not include -3 (or +3), so there will be open circles at those two points.

Answer 8

to show which points are allowed, those points on the number line will be shaded in with a dark line.

Answer 9

Is this how the graph would look like?

Answer 10

people also use a "rule" : if you multiply both sides by -1, "flip" the relation so 3 > -x becomes -3 < x but if you only add, you don't have to remember this rule

i second this !

Answer 11

to pick the correct graph, first ask yourself, is x=0 allowed ?

in other words is -3 < 0 ?
is 0 < 3 ?

Answer 12

is 0 bigger than -3 ? (is 0 degrees warmer than -3 below 0 ?)
is 0 less than 3 ?

Answer 13

0 is not bigger than -3 but its less than 3

Answer 14

0 is bigger than -3

maybe that doesn't seem clear, but if you think of it as temperature, 0 degrees outside is warmer than -3 degrees.

Answer 15

or, if you think of it as money, -3 means you owe 3, 0 means you owe nothing, +3 means you have 3
so in order of how much you have: -3, 0, 3 (things are better for you as you go from -3 to 0 to +3)

Answer 16

If not clear, see
http://www.khanacademy.org/math/arithmetic/absolute-value/add-sub-negatives/v/negative-numbers-introduction

Answer 17

I am just not sure about the graph :( still so confused

Answer 18

Sorry!

Answer 19

First, x can be 0, because -3 < x < 3 is true for x=0
-3 < 0 < 3 is true

so you should look for a graph that has a line the includes 0
the graph should have an open circle on the -3 and on the +3

Answer 20

Like this?

Answer 21

yes

Answer 22

Thanks a lot for everything!!!! :D

Answer 23

you could have checked x=1
is -3 < 1 and 1 < 3
yes. 1 is bigger than -3 and 1 is less than 3
so you could look for a graph that has a line that includes x=1 (or any x between -3 and 3)
you would get this same graph

Answer 24

THANKS A LOT!!!!