Question

I’m confused on what’s going on here, so if someone could explain it I would be super grateful.

Answer 1

Range of x

$-\frac{1}{5} <x <4$ and x>6

Step-by-step explanation:

Given AB = 4x + 5, BC = 3x - 2 and AC 9x -5

The sum of the length of any two sides of a triangle is greater than the length of third side.

Case I

AB + BC > AC

⇔4x +5 +3x -2 > 9x -5

⇔7x + 3 >9x - 5

⇔ 7x -9x > -5 -3

⇔-2x > -8

⇔x <4

Case II

if AB+AC > BC

4x +5 +9x -5> 3x -2

⇔13x >3x -2

⇔ 13x -3x> -2

⇔10x > -2

⇔x >$-\frac{1}{5}$

Case III

AC+BC > AB

⇔9x - 5 +3x - 2 > 4x +5

⇔6x -7 > 4x +5

⇔6x -4x >5+7

⇔2x > 12

⇔x > 6