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