Need help now pls

Question

Point U is on line segment \overline{TV}TV. Given TU=4,TU=4, UV=5x,UV=5x, and TV=3x+6,TV=3x+6, determine the numerical length of \overline{TV}.TV

Answer 1

First, note that:

TV = TU + UV, so:

3x + 6 = 4 + 5x

-3x - 4 = -4 - 3x

0 + 2 = 0 + 2x

2 = 2x

1 = x

So, TV = 3x + 6 = 3*1 + 6 = 3 + 6 = 9.

Answer 2

I recommend following my explanation by drawing a picture.

Draw a line, and label the left endpoint T and the right endpoint V. We as mathematicians call this line "TV".

Somewhere along line TV, draw a new point on the line; label it U.

Now we must label the measurements that are given to us:

Label the line segment that connects only T and U, to be 4.

Similarly, label the line segment that connects only U and V, to be 5x.

Now let's talk about how to solve the problem, that is to find the length of segment TV:

You are given that TV is in total 3x+6. But we know that TV is made up of segments TU and UV. Therefore, we can form this equation:

TU + UV = TV

Plugging in the measurement of each segment, we get:

4 + 5x = 3x + 6.

Now, solve for x, and plug x into 3x + 6 to get your answer -- the length of TV.

---

For your next problems, I recommend looking back at your notes to see if your teacher gave you examples to follow. They will look similar to what we just did here. Best of luck!