Inequalities

Solve 3 < l X - 5 l .

When I graph this I can see the answer is 2 < X < 8

But when I try to sovle it as an inequality it doesn't work. What am I doing wrong?

3 < X -5

X > 8

3 < -x + 5

X < 2

Victoria (Worried)

Quote:

---

Originally Posted by Vicky1997

Solve 3 < l X - 5 l .

When I graph this I can see the answer is 2 < X < 8

But when I try to sovle it as an inequality it doesn't work. What am I doing wrong?

3 < X -5

X > 8

3 < -x + 5

X < 2

Victoria (Worried)

---

Hi Victoria,


Remember this: If |a| > b, then a > b or a < - b.

So, your algebra is correct. Check your graphing techniques again.

x - 5 > 3 or x - 5 < -3

Solving these two inequalities results in x > 8 or x < 2.

Thanks. I see I misread the graph.

So you have 3 < |x-5|
First of all you must define the module function:
|x-5|= x-5 , for x-5>=0, meaning for x>=5
|x-5|= 5-x , for x-5<0, meaning for x<5

So we go on with the inequality on two sides:
We take first x>=5. We have 3<x-5 =>x>3+5=>x>8. And because x is supposed to be greater than 5, we have the final partial solution: x>8.

Next, we have x<5. Our inequality becomes: 3<5-x=>x<5-3=>x<2. Because x<5, the final second partial solution is x<2.

This is the last result.