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M is the midpoint of the segment. Find the indicated length. XM=2x+35, MZ=5x-22 find XZ

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Final answer:

To find the length XZ, set up an equation with XM and MZ. Solve the equation to find the value of x. Substitute the value of x back into XM to find the length of XZ.

Step-by-step explanation:

To find the length XZ, we can use the fact that M is the midpoint of the segment. This means that XM and MZ are equal in length. So, we can set up the equation 2x+35 = 5x-22 where 2x+35 represents XM and 5x-22 represents MZ. Now, we can solve this equation to find the value of x.



2x+35 = 5x-22

35 + 22 = 5x - 2x

57 = 3x

x = 57/3

x = 19



Now that we have found the value of x, we can substitute it back into either XM or MZ to find the length of XZ. Let's substitute it into XM:



XM = 2x+35 = 2(19)+35 = 38+35 = 73



Therefore, the length of XZ is 73.

User Mujadid Mughal
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