Step-by-step explanation:
Imagine this segment, given that m is the midpoint of segment JK...
J________M________K
JM = 7x-32 MK = 89 - 4x (given)
If m is the midpoint, then JM and MK are the same lengths (equal to each other). We can use that to first find what x is.
[tex]7x -32 = 89 - 4x\\[/tex]
Steps to find x (we have to get x by itself):
[tex]7x - 32 + 4x = 89 - 4x +4x[/tex]
[tex]11x -32 = 89[/tex]
[tex]11x -32 +32 = 89 +32[/tex]
[tex]11x = 121[/tex]
[tex]\frac{11x}{11} = \frac{121}{11}[/tex]
[tex]x=11[/tex] (we haven't found the answer yet! we only found x)
Now that we found x, we can find segment MK. Now we know that:
[tex]MK = 89 - 4x[/tex]
[tex]x= 11[/tex]
Let's plug x into the equation:
[tex]MK = 89 - 4(11)\\MK = 89- (44)\\MK = 45[/tex]
Answer: [tex]MK= 45[/tex]
