Question

PLEASE HELP ASAP!!!!!!!!!!!!!!

Rewrite each of the following expressions without using absolute value
1.|x-1| if x>1
2. |x-y| if x>y
3. |3-
`√(4)`
4. |4r -12| if r<3
5. |
`√(15) -5+1`
6. |4-
`√(7)`
7. |7m-56| if m<8
8. |z-7|-|z-9| if z<7

Answer 1

1 4(3-r) or 12-4r

2. 7( 8-m) or 56-7m

3. -2

Explanation:

1) |4r−12| , if r<3

|4r-12|

Factor out a 4

4|r-3|

|r-3| will be less than 0 since r is less than 3

So we can rewrite it as 3-r to remove the absolute value signs and make it positive

4 (3-r)

12 -4r

2. |7m–56| , if m<8

Factor out a 7

7| m-8|

|m-8| will be less than 0 since m is less than 8

So we can rewrite it as 8-m to remove the absolute value signs and make it positive

7( 8-m)

56-8m

3) |z−7|−|z−9| , if z<7

|z-7| will be less than 0 since z is less than 7 and |z-9| will be less than 0 since z is less than 7

So we can rewrite it as 7-z and 9-z to remove the absolute value signs and make it positive

7-z - (9-z)

Distribute the minus sign

7-z-9+z

-2