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Answer:

Line NMLK: x = 13

Line STUF: x = 15

Step-by-step explanation:

Line NMLK:

Using our knowledge of algebra, we can turn this into an equation that is simpler. The full length of line NMLK is 23, so we will set the equation equal to 23. On the other side of the equation will be the remaining variables.

x - 6 + 9 + 2x - 19 = 23

Start by adding -19, -6, and 9 together to get:

x + 2x - 16 = 23

Add 16 to both sides and add the like variables together (x's).

3x = 39

39 ÷ 3 = 13

Therefore, x = 13.

To check we can plug it into our original equation

13 - 6 + 9 + 2(13) - 19 = 23

7 + 9 + 26 - 19 = 23

7 + 9 + 7 = 23

16 + 7 = 23

23 = 23

Therefore the answer checks out!

Line STUF

Now we will do the same with the line STUF.

13 + 6 + 2x - 18 = 4x - 29

We will add all like terms together.

1 + 2x = 4x - 29

Next we will subtract 2x from 4x.

1 = 2x - 29

Then we will add 29 to 1 which gives us:

30 = 2x

Divide by 2.

x = 15

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