solving inequalitys for 'x'
- Thread starter TStiles4
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arthur ohlsten
Full Member
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replace I x -5 I >1 with two equations , one for x>5 , and one for x<5
x-5>1 for x>5
x>6 for x>5
x>6 then I x-5 I>1 answer
-[x-5]>1 for x<5
-x+5>1
4>x
I x-5I >1 for x<4
-oo <x<-4 and 5 <x <oo annswer
Arthur
x-5>1 for x>5
x>6 for x>5
x>6 then I x-5 I>1 answer
-[x-5]>1 for x<5
-x+5>1
4>x
I x-5I >1 for x<4
-oo <x<-4 and 5 <x <oo annswer
Arthur
mmm4444bot
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- Oct 6, 2005
- Messages
- 10,962
Start by getting rid of the absolute-value symbols.
To state that the absolute value of some expression is greater than 1 means that this value is located more than one unit away from zero on the Real number line. But we can move away from zero in two different directions, so we need to consider both cases.
|expression| > constant
means:
expression > constant
OR
expression < -constant
Here's an example.
|x + 3/5| > 20
The solution set for this absolute-value inequality will be all numbers x that after being increased by three-fifths are located more than 20 units away from zero (in either direction).
To get rid of the absolute-value symbols, we write the two inequalities shown above.
x + 3/5 > 20
OR
x + 3/5 < -20
Now we solve each of these separately.
x > 97/5
OR
x < -103/5
If your instructor wants interval notation, then this solution can be written like so:
(-infinity, -103/5) U (97/5, infinity)
Let us know, if you still have questions about your exercise. Please show your work, or explain why you think you're stuck.
To state that the absolute value of some expression is greater than 1 means that this value is located more than one unit away from zero on the Real number line. But we can move away from zero in two different directions, so we need to consider both cases.
|expression| > constant
means:
expression > constant
OR
expression < -constant
Here's an example.
|x + 3/5| > 20
The solution set for this absolute-value inequality will be all numbers x that after being increased by three-fifths are located more than 20 units away from zero (in either direction).
To get rid of the absolute-value symbols, we write the two inequalities shown above.
x + 3/5 > 20
OR
x + 3/5 < -20
Now we solve each of these separately.
x > 97/5
OR
x < -103/5
If your instructor wants interval notation, then this solution can be written like so:
(-infinity, -103/5) U (97/5, infinity)
Let us know, if you still have questions about your exercise. Please show your work, or explain why you think you're stuck.
mmm4444bot
Super Moderator
- Joined
- Oct 6, 2005
- Messages
- 10,962
arthur ohlsten said:
Mr. Ohlsten:
Why do you continue to complete students' homework for them?
By the way, neither x>5 nor x<5 are equations.
I think, in general, you do more damage here than good.
(I'm about to give up at this site because of you and those here like you. If I make such a decision, then go ahead and feel free to think that you've "won".)
TStiles4 said:
It might help you to recognize that "absolute value" means "distance from 0 on the number line."
So, the inequality
| x - 5 | > 1
tells us that (x - 5) is MORE than 1 unit from 0 on the number line. Where does that put (x - 5)?
MORE THAN 1 unit to the right of 0 means that (x - 5) > 1.
MORE THAN 1 unit to the left of 0 means that (x - 5) < -1
So...
you have two inequalities to solve.
(x - 5) > 1, OR (x - 5) < -1
Solve those inequalities and you'll have the regions on the number line which constitute the solution for your original inequality.