# Find XZ, if XM = 2x + 35 and MZ = 5x - 22.?

Relevance
• Pope
Lv 7
1 month ago

Either MXZ is a triangle or points M, X, and Z are collinear.

If MXZ is a triangle, |XM - MZ| < XZ < XM + MZ.

If M, X, and Z are collinear, XZ = |XM - MZ| or XZ = XM + MZ.

Combining the two cases,

|XM - MZ| ≤ XZ ≤ XM + MZ

|(2x + 35) - (5x - 22)| ≤ XZ ≤ (2x + 35) + (5x - 22)

|57 - 3x| ≤ XZ ≤ 7x + 13

• 1 month ago

If XM = 2x + 35 and MZ = 5x - 22, find XZ.

XZ = 7x + 13.

If M is the midpoint of XZ:

2x + 35 = 5x - 22

3x = 57

x = 19

XZ = 146

• 1 month ago

You haven't told us anything about the relationship of X, M and Z.

I'm going to assume they are on a line where XM + MZ = XZ

I'm also going to assume that M is the midpoint.

That means the two segments are equal in length.

5x - 22 = 2x + 35

Get like terms together:

5x - 2x = 35 + 22

3x = 57

x = 57/3

x = 19

Now plug that into either equation:

5x - 22

= 5(19) - 22

= 95 - 22

= 73

And the other segment would have the same length. Let's calculate it to be sure:

2x + 35

= 2(19) + 35

= 38 + 35

= 73

Adding those together we get the length for XZ.

XZ = XM + MZ

XZ = 73 + 73

XZ = 146

P.S. Next time please provide the full information so that we don't have to guess and make assumptions. :)