32.
so, the two dashes on the lines, the | represent those two portions are equal. also it alr says that MN is the segment bisector, and bisector means that something is split in half.
so, this basically means we can set 3x+1 and 8x-24 equal to each other
3x+1=8x-24
so we need to split up the numbers so x is on one side. the easiest way to do this is to move the -24 to the other side. to do this, we need to balance the equation. if we move one thing to one side, we need to flip the sign. so -24 is negative, so we need to make it +24 and add it to 1
3x+25=8x
now, move 3x to the other side, but since it’s positive, make it -3x. subtract it from 8x
25 = 5x
now, x is attached to 5 by multiplication so we need to do the opposite of multiplication, division. divide 25 by 5 to isolate x
5 = x
so since x = 5, we can plug it back in to any of the segments ill pick 3x+1
3(5)+1
that equals 16
since we know both lines are equal in length, we can double 16, which equals 32