Question

Mis the midpoint of segment AB. If AM = 6x – 25 and MB = 3x + 14. Solve for x.

A) x = 6
B) x = 3.6
C) x = 4.3
D) x = 13

Answer 1

To solve for x, we set the lengths of AM and MB equal since M is the midpoint, resulting in the equation 6x - 25 = 3x + 14. We simplify this to find that x = 13, which is option D.

Step-by-step explanation:

If M is the midpoint of segment AB and the lengths of AM and MB are given by the expressions AM = 6x – 25 and MB = 3x + 14, then these two segments must be equal in length because a midpoint divides a segment into two equal parts. To solve for x, set the expressions for AM and MB equal to each other:

6x – 25 = 3x + 14

Now solve for x by combining like terms and isolating x on one side of the equation:

6x – 3x = 14 + 25

3x = 39

x = 39 / 3

x = 13

Therefore, the value of x that satisfies the equation is 13, which corresponds to option D.