In segment AC, the midpoint is B. If segments AC = 5x-9 and AB = 2x, what is the measure of segment AC.

 To find the measure of segment AC when B is the midpoint, you should realize that when B is the midpoint, segment AB is equal to segment BC. Given that AC is the entire segment from A to C, it can be divided into two equal parts by the midpoint B. Therefore, AB = BC.

We are told that AB = 2x and AC = 5x - 9. Since AB = BC (because B is the midpoint), we can express AC as AB + BC. Based on our information this leads to:

AC = AB + BC AC = 2x + 2x (since AB = BC) AC = 4x

Now we can set the two expressions for AC equal to one another because they represent the same segment:

4x = 5x - 9

To solve for x, we need to get all the terms with x on one side and the constant on the other. We can do this by subtracting 4x from both sides:

4x - 4x = 5x - 4x - 9 0 = x - 9

Next, we isolate x by adding 9 to both sides:

x = 9

Now that we have the value of x, we can find the measure of segment AC:

AC = 5x - 9 AC = 5(9) - 9 AC = 45 - 9 AC = 36

The measure of segment AC is 36.