Question

Point B lies between points A and C on line AC. Let x represent the length of segment AB in inches.

Use the segment to complete the statements.
1. The value of x is __.
2. The length of line AB in inches is __.
3. The length of BC in inches is __.

Answer 1

Part 1) The value of x is 5

Part 2) The length of line AB is 5 inches

Part 3) The length of BC is 15 inches

Answer 2

Part 1) The value of x is 5

Part 2) The length of line AB is 5 inches

Part 3) The length of BC is 15 inches

Explanation:

see the attached figure to better understand the problem

Part 1) Find the value of x

we know that

`AC=AB+BC` -----> equation A

we have

`AB=x\ in`

`BC=3x\ in`

`AC=20\ in`

substitute the values in the equation A and solve for x

`20=x+3x`

`20=4x`

`x=5`

Part 2) Find the length of line AB

we know that

`AB=x\ in`

substitute the value of x

`AB=5\ in`

Part 3) Find the length of BC

we know that

`BC=3x\ in`

substitute the value of x

`BC=3(5)=15\ in`