Question

Andre's house, the middle school, and the library are along the same street. The middle school

is between Andre's house and the library. The distance between Andre's house and the middle
school is x + 3, and the distance between the middle school and the library is 4x + 12.
Use the following diagram to write and simplify an expression for the distance between
Andre's house and the library.

PLS HELP!!!!!!​

Answer 1

x+3+4x+12

Explanation:

WIK:

. Andres house, the middle school and the library are along the same street.

. The middle school is between Andre's house and the library.

.The distance between Andre's house and the middle

school is x+3

. The distance between the middle school and the library is 4x+12

That means that you have to add x+3 + 4x + 12, since the distance between the middle school is between Andre's house and the library is x+3, and the distance between the middle school and the library is 4x+12. That means we have to add since the middle school and the library are along the same street.

Answer 2

The expression for the distance between Andre's house and the library is

`(5x+15)`

Explanation:

Let

A -----> Andre's house

B ----> Middle school

C ----> Library

see the attached figure to better understand the problem

we know that

`AC=AB+BC` -----> by addition segment postulate

we have

`AB=(x+3)\ units` -----> distance between Andre's house and the middle school

`BC=(4x+12)\ units` -----> distance between the middle school and the library

substitute

`AC=(x+3)+(4x+12)`

Combine like terms

`AC=(5x+15)\ units`

therefore

The expression for the distance between Andre's house and the library is

`(5x+15)`