Question

Point B is the midpoint of segment ACIf AB=5x and BC=3x+14, find x and the length of AC

Answer 1

To solve this, let's use a rough sketch of the data for more clarity.

Since AB is the midpoint of BC, then:

5x = 3x + 14

5x - 3x = 3x - 3x + 14

2x = 14

Dividing both sides by 2,

`\begin{gathered} (2x)/(2)=(14)/(2) \\ x=7 \\ AC\text{ = 5x + 3x +14} \\ AC\text{ = 8x + 14} \\ x=7, \\ AC=8(7)+14 \\ AC=56\text{ + 14} \\ AC=70 \end{gathered}`

In summary, the value of x is 7 unit and AC is 70 unit.