Question

draw a picture to represent the following description and solve. if a segment lm is bisected at a point n, and ln = 9x - 2 and nm = 5x + 14, what is x? what does equidistant mean?

Explanation:

Step1: Set up the equation

Since point N bisects segment LM, LN = NM. So, $9x - 2=5x + 14$.

Step2: Subtract 5x from both sides

$9x-5x - 2=5x-5x + 14$, which simplifies to $4x-2 = 14$.

Step3: Add 2 to both sides

$4x-2 + 2=14 + 2$, resulting in $4x=16$.

Step4: Solve for x

Divide both sides by 4: $\frac{4x}{4}=\frac{16}{4}$, so $x = 4$.

For the second - part:

In geometry, equidistant means being at an equal distance. For example, a point on the perpendicular bisector of a line segment is equidistant from the two endpoints of the line segment.

Answer:

In geometry, it means being at an equal distance.