Geometry Help with problem

Question

Point A is the mid point of MN. MA=3x+1 and MN=7x-13

What is the length of AN?

Answer 1

In this problem, we have a line segment MN with A exactly in the middle. This creates two segments, MA and AN that are congruent. We are told that MA = 3x+1, so AN also = 3x+1. We also know that if we add MA and AN together, we will get the entire length of the line which is MN.

Now, we can write an equation summarizing this information:

MA + AN = MN

3x + 1 + 3x+1 = 7x - 13

Now, you can use algebra to solve for x. Then plug your answer for x back into the equation for MA (since it is the same as AN) to find the answer to the question.