Final answer:
To find x when line l bisects segment AB and AM is equal to MB, the equation 2x=2AM is used, giving x=AM. If AB's total length is known, substituting it into AB=2x divided by 2 gives the value of x and the lengths of AM and MB.
Step-by-step explanation:
When line l bisects segment AB, it means line l divides AB into two equal parts, so AM = MB. We are given that AB=2x and that AM=MB. Since AM and MB are equal, we can express AB as 2AM or 2MB.
To find the value of x, set up the equation 2x = 2AM. Because the segment is bisected, AM is equal to MB, and AB = AM + MB, we can simplify this to x = AM (or MB). Thus, to solve for x from AB=2x and AM=MB, we set 2AM = 2x, and dividing both sides by 2 gives us AM = x. Then, since AB is twice the length of AM, 2x = AB, we can substitute AM for x to find that AB = 2AM, which means AB is twice the length of AM.
Therefore, AB=2x can be divided by 2 to get AB/2 = x. Substituting the total length AB back into the equation, if we know it, would give us the specific value for x and thus for AM and MB.