The problem asks us to find the value of $x$, given that segments $NL$ and $NM$ are tangent to the circle and that $NL = 7x - 3$ and $NM = 18$.

1. Problem Description

The problem asks us to find the value of $x$, given that segments $NL$ and $NM$ are tangent to the circle and that $NL = 7x - 3$ and $NM = 18$.

2. Solution Steps

If two segments are tangent to a circle from the same exterior point, then the segments are congruent.

Therefore, $NL = NM$.

We are given $NL = 7x - 3$ and $NM = 18$.

So, we have the equation $7x - 3 = 18$.

Add 3 to both sides:

$7x - 3 + 3 = 18 + 3$

$7x = 21$

Divide both sides by 7:

$\frac{7x}{7} = \frac{21}{7}$

$x = 3$

3. Final Answer

The value of $x$ is 3.