Answer: x = 10
Step-by-step explanation:
Since L is the midpoint of HK (because HL ≅ KL)
and M is the midpoint of IJ (because IM ≅ JM)
then LM is the "average" of the bases HI and KJ.
[tex]\dfrac{HI+KJ}{2}=LM\\\\\\\dfrac{(4x-3)+(x+11)}{2}=3x-1\\\\\\4x -3 + x + 11 = 2(3x-1)\quad \rightarrow \quad \text{multiplied both sides by 2}\\\\5x+8=6x-2\quad \rightarrow \quad \text{added like terms and distributed right side}\\\\.\qquad 8=x-2\quad \rightarrow \quad \text{subtracted 5x from both sides}\\\\.\qquad 10=x\quad \rightarrow \quad \text{added 2 to both sides}[/tex]
