Final answer:
No provided option matches the solution for the length of LN based on the given values. With LM being 37 units and MN being 3x−7 units, the length of LN would be 3x + 30 units, indicating a possible mistake in the options or the values provided in the original question.
Step-by-step explanation:
The student is asking about the length of a line segment LN when given the lengths of segments LM and MN as expressions involving x. To solve this, we must recognize that line segment LN is the sum of segments LM and MN. We are given that LM is 37 units long and MN is 3x−7 units long.
Therefore, we add the expressions for LM and MN to find LN:
- LN = LM + MN
- LN = 37 + (3x−7)
- LN = 37 + 3x − 7
- LN = 3x + 30
From the expressions provided as options, none match the expression we found for LN. This indicates that there may be a typo or mistake in the provided options or in the original values given for LM and MN. In any case, with the provided information, the correct expression for LN in terms of x should be 3x + 30 units long.