Solve Inequality: Interval Form Answer | x ∈ [-4, 4]

[MrNeWBiE]

Homework Statement

Solve the inequality and write your answer in interval form.

2x+1 <= 5- x < x-7

The Attempt at a Solution

fist part 2x+1 <= 5- x
-4 <= -x
4 >= x

second part

5- x < x-7
0<-12 ,,,,,,,,,, O,O how it's gone be like this ?

well if it's right how i can write it in interval form ?

 

[tiny-tim]

Hi MrNeWBiE

(have a ≤ )

fist part 2x+1 <= 5- x
-4 <= -x
…
5- x < x-7
0<-12

No, both these are wrong, for the same reason:

when you transfer -x across an = or ≤, you must multiply it by -1.

 

[MrNeWBiE]

ohhhh i see it now ,,,

2x+1 ≤ 5- x

-4≤-3x

x≤4/3

5- x < x-7
-2x<-12 ...x>6

now they are right ?

yet i didn't understand you ,,,,,

 

[tiny-tim]

Yup!

(I just meant that when you move -x across, it becomes +x, as you've done)

And now express that it interval form (you may need to use ∞).

 

[MrNeWBiE]

(-∞,4/3]U[4/3,6) right ,,, ? or it's to ∞ not 6 ...

 

[tiny-tim]

(-∞,4/3]U[4/3,6) right ,,, ?

That's just (-∞,6)

or it's to ∞ not 6 ...

and that's (-∞,∞).

 

[MrNeWBiE]

i know that ,,,

but our tacher keep asking for more details ,,,,

if i write like this " (-∞,6) " he will say where is the 4/3 and the same for the other ,,, >.<

 

[tiny-tim]

if i write like this " (-∞,6) " he will say where is the 4/3

Yes, and that's because (-∞,6) is wrong!

Go back to x≤4/3

...x>6.

 

[MrNeWBiE]

x>6 how it's gone be x≤4/3 ,,,

isn't 6>4/3 ,,,=p

how x > 6 then x≤4/3 ??

 

[tiny-tim]

x>6 how it's gone be x≤4/3 ,,,

isn't 6>4/3 ,,,=p

how x > 6 then x≤4/3 ??

Exactly!

So that means … ?

 

[MrNeWBiE]

no answers maybe ...

 

[tiny-tim]

Looks like it!

 

[MrNeWBiE]

thx xD

sorry for wasting your time