Answer:
AC = 58 units
Explanation:
Pre-Solving
We are given line segment AC, which is bisected by line y, and that AB = 5x-1 and BC = 7x-13.
Recall that a bisector divides a line into two parts.
This means that that the parts created by the bisector, AB and BC are equal to each other.
This means that 5x-1 = 7x-13.
Solving
We can solve 5x - 1 = 7x - 13
Start by adding 13 to both sides.
5x + 12 = 7x
Subtract 5x from both sides.
12 = 2x
Divide both sides by 2.
6 = x
We found the value of x, however we aren't done yet, as we want to find the value of AC.
Since AB and BC are the two parts that make up the bisector, we can add their values up together to get the value of AC.
So,
AC = AB + BC
AC = 5x - 1 + 7x - 13
AC = 12x - 14
Substitute 6 for x.
AC = 72 - 14
AC = 58
AC is 58 units.