Question

sketch intervals described by given inequalities:
lx- 1/2 l < 1

Answer 1

I'm assuming that it's \[\large \left| x-\frac{ 1 }{ 2 } \right|<1\]

So remember that absolute value is DISTANCE FROM 0. So if some {stuff} has to be LESS THAN a units from 0 (a is a distance here so has to be positive), what that really means is that the stuff satisfies:

\[\large -a<stuff<a\]

Answer 2

yes it is haha sorry about that, I dont know how to type it onto the computer

Answer 3

So for example\[\large \left| t \right|<7 \]really means \rightarrow -7<t<7\[ -7<t<7\] since in order for t to be within 7 units of 0, it must be between -7 and +7. right?

Answer 4

(that's ok - that's exactly what you typed but I just wanted to confirm, because sometimes people DON'T mean exactly what they type! lol)

Answer 5

oh haha, okay.

okay so the 0 is about one unit, or point, away ?

Answer 6

@DebbieG Okay, so .... I get this then \[1/2 < 0 > 1 \frac{ 1 }{ 2 } ? Right?\]

Answer 7

\[\left| x-\frac{ 1 }{ 2 } \right|<1\]
\[-1 < x-\frac{ 1 }{ 2 } <1\]

then you add 1/2 to all sides. what do you get?

Answer 8

^^ right.... what @surdawi said. Your inequality can NEVER have the inequality signs going in opposite directions, that's a big no-no!

Answer 9

i get \[-\frac{ 1 }{ 2 } <x >1\frac{ 1 }{ 2 }\]

Answer 10

oh haha I didnt notice I did opposite signs

Answer 11

why do you flip the inequality sign ?

Answer 12

I pressed the wrong button, sorry @surdawi

Answer 13

No.... look at my example above.

if |stuff|<a then -a<stuff<a

1. the inequalities go in the same direction
2. the STUFF is exactly what was inside the absolute value
3. use -a on the left and a on the right.

Answer 14

THEN solve that compound inequality by isolating the variable in the middle.

Answer 15

ya, so its
- 1/2 < x < 1 1/2; right?

Answer 16

Yes, there you go. :)

Answer 17

so x> -1/2
and x< 1 1/2 ?

Answer 18

so by showing these calculations, is this is what it means to sketch or would I have to sketach a number line?

Answer 19

Write. If you are to graph it on a number line, you draw in the line between those two numbers. Since it is a strict inequality, you should have a "()" at each endpoing (or an open circle) to indicate that the endpoint is not included.