Answer:
[tex] \displaystyle x = 15[/tex]
Step-by-step explanation:
by triangle midsegment theorem we obtain:
[tex] \displaystyle \frac{10x + 44}{2} = 8x - 23[/tex]
simplify division:
[tex] \displaystyle 5x + 22 = 8x - 23[/tex]
move 5x to right hand side and -23 to the left hand side and change its sign:
[tex] \displaystyle 22 + 23= 8x - 5x[/tex]
simplify addition:
[tex] \displaystyle 8x - 5x = 45[/tex]
collect like terms:
[tex] \displaystyle 3x = 45[/tex]
divide both sides by 3:
[tex] \displaystyle x = 15[/tex]
and we are done!
