Question

Point V lies between points U and W on .

If UW = 9x – 9, what is UW in units?

5 units
6 units
30 units
36 units

Answer 1

The length of UW in units is:

36 units.

Explanation:

It is given that:

Point V lies between points U and W on.

This means that the length of the line segment UW is equal to the sum of the length of the line segment UV and VW.

i.e.

`UW=UV+VW`

i.e.

`9x-9=2x-4+4x+10`

on combining the like terms in the right hand side of the expression we have:

`9x-9=2x+4x-4+10\\\\9x-9=6x+6`

Now on combining the like terms we have:

`9x-6x=6+9\\\\i.e.\\\\3x=15\\\\x=(15)/(3)\\\\x=5`

Hence,

`UW=9* 5-9\\\\i.e.\\\\UW=9(5-1)\\\\i.e.\\\\UW=9* 4\\\\UW=36`

Answer 2

36 units

Explanation:

From the diagram |UW|=|UV|+|VW|

We the expressions in terms of x to get:

`9x - 9 =( 2x - 4 )+ (4x + 10)`

We group the similar terms to get:

`9x - 2x - 4x = - 4 + 10 + 9`

`3x = 15`

Divide both sides by 3

`(3x)/(3) = (15)/(3)`

`x = 5`

`\implies \: |UW| = 9(5) - 9 = 45 - 9 = 36`