Distance on a number line is modeled with absolute value. The distance between a position $x$ and the marker at $7$ is $|x-7|$. Since the sensor detects motion at points exactly $11$ meters away, the equation is

This equation gives two possible positions, one $11$ units to the left of $7$ and one $11$ units to the right.

Being exactly 3^0\text{C} away from the target temperature of 18^0\text{C} means

So the possible temperatures are

The problem also says the reading was above 16^0\text{C}, so $15$ does not work. Therefore, the value of $x$ could be $21$.

Break the expression into intervals based on where the absolute values change sign: at $x=-2$ and $x=4$.

If $x\le -2$, then

So,

Set this equal to $10$:

which fits this interval.

If $-2\le x\le 4$, then

So,

Since $6\ne 10$, there are no solutions in this interval.

If $x\ge 4$, then

So,

Set this equal to $10$:

which fits this interval.

There are $2$ real solutions, so the correct answer is $2$.

Since $4-x=-(x-4)$, the expressions $|4-x|$ and $|x-4|$ are equal because absolute value makes opposites have the same value. So

Therefore, the equivalent expression is $2|x-4|$.

Set the two expressions for $y$ equal:

Adding $3$ to both sides gives

This means $x-4=5$ or $x-4=-5$, so the intersection points have $x$-coordinates $9$ and $-1$. Since both points lie on the horizontal line $y=2$, the distance between them is the difference in their $x$-coordinates: