Answer:
[tex]8\ units< x < 18\ units[/tex]
Step-by-step explanation:
we know that
The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side
so
Applying the Theorem
case 1) [tex]42+4x > 2x-6[/tex]
[tex]4x-2x > -6-42[/tex]
[tex]2x > -48[/tex]
[tex]x > -24\ units[/tex]
case 2) [tex]42+(2x-6) >4x[/tex]
[tex]42-6 >4x-2x[/tex]
[tex]36 >2x[/tex]
[tex]18 >x[/tex] -----> rewrite
[tex]x<18\ units[/tex]
case 3) [tex]4x+(2x-6) > 42[/tex]
[tex]4x+2x > 42+6[/tex]
[tex]6x > 48[/tex]
[tex]x > 8\ units[/tex]
therefore
[tex]8\ units< x < 18\ units[/tex]
