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If line y bisects AC. AB= 5x-1, and BC = 7x-13, find AC

User DenLanden
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1 Answer

5 votes

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.

User Jarnojr
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