Question

Point M is the midpoint of AB . AM= 3x+3, and AB=8x−6

Answer 1

Answer:

The length of AM is:

                                21 units.

Step-by-step explanation:

Point M is the midpoint of AB.

AM= 3x+3, and AB=8x−6

Since, the midpoint divides the line segment into two equal parts i.e. it bisects the line segment.

Hence, we have:

                         AM+MB=AB

Also, AM=MB

Hence, we have:

     $3x+3+3x+3=8x-6$

on combining the like terms in the left hand side of the equation we have:

$3x+3x+3+3=8x-6\\\\6x+6=8x-6$

Now, on subtracting both side of the equation by 6x we have:

$6=8x-6-6x\\\\6=8x-6x-6\\\\6=2x-6$

on adding 6 on both side of the equation we have:

$6+6=2x\\\\12=2x\\\\2x=12\\\\x=\dfrac{12}{2}\\\\x=6$

Hence, we have:

$AM=3\times 6+3\\\\AM=21\ \text{units}$

Answer 2

AM= Half of AB

or, 3x+3=(8x-6)/2
or, 6x+6=8x-6
or, 2x=12
Therefore,x=6

so,AM=3*6+3=21