SOLUTION: I'm actually helping a friend in Trig and I forgot absolute value. The question is below. Solve for x: 2|-x+4| > 10 1. {x | 1 < x < 9} 2. {x | x < 1 or x > 9} 3. {x | x < -

Algebra ->  Absolute-value -> SOLUTION: I'm actually helping a friend in Trig and I forgot absolute value. The question is below. Solve for x: 2|-x+4| > 10 1. {x | 1 < x < 9} 2. {x | x < 1 or x > 9} 3. {x | x < -      Log On


   

Question 857314: I'm actually helping a friend in Trig and I forgot absolute value. The question is below.
Solve for x: 2|-x+4| > 10
1. {x | 1 < x < 9}
2. {x | x < 1 or x > 9}
3. {x | x < -9 or x > -1}
4. {x | x < -1 or x > 9}
Found 2 solutions by richwmiller, Edwin McCravy:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
2|-x+4| > 10
|-x+4| > 5
4. {x | x < -1 or x > 9}
treat as if it were
2 sqrt((4-x)^2)>10
sqrt((4-x)^2)>5
4-x>+ or -5
4-x>+5
-x>1
x<-1
4-x>-5
-x>-9
x>9
4. {x | x < -1 or x > 9}




Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

2|-x+4| > 10 

Divide both sides by 2

|-x+4| > 5

|Y| > 5 has solution interval 

{Y < -5 or Y > 5}

Therefore if we let Y = |-x+4| 

|-x+4| > 5 has solution interval 

{-x+4 < -5 or -x+4 > 5} 

Add -4 to both sides of both inequalities:

{-x < -9 or -x > 1}

Divide both inequalities by -1, remembering that
when an inequality is divided through by a negative,
the inequality symbol is reversed:

{x > 9 or x < -1}

That is the same as the solution interval for this
solution set: 

4. {x | x < -1 or x > 9}  

Edwin