Answer:
AB is 31.
Step-by-step explanation:
So we know that B is the midpoint of AC. This means that:
[tex]AB=BC[/tex]
by the definition of midpoint.
We know that AB is 2x+1 and BC is 5x-44. Substitute:
[tex]2x+1=5x-44[/tex]
Now, find the value of x.
Subtract 1 from both sides:
[tex]2x=5x-45[/tex]
Subtract 5x from both sides:
[tex]-3x=-45[/tex]
Divide both sides by -3:
[tex]x=15[/tex]
So, the value of x is 15.
AB is 2x+1.
Substitute 15 into x. So:
[tex]AB=2(15)+1[/tex]
Multiply:
[tex]AB=30+1[/tex]
Add:
[tex]AB=31[/tex]
So, the length of AB is 31.
And we're done!
