Posted by eve on Saturday, May 5, 2012 at 3:36pm.
| x - 4 |-| 7 - x | = 1
| x - 4 | = 1 + | 7 - x |
Eliminate the absolute values:
First equation :
( - ( x - 4 ) ) = ( 7 - x ) + 1
Second equation :
( x - 4 ) = ( 7 - x ) + 1
Third equation :
( x - 4 ) = ( - ( 7 - x ) ) + 1
Fourth equation :
( x - 4 ) = ( 7 - x ) + 1
You have equation ( x - 4 ) = ( 7 - x ) + 1 twice.
So you must solve 3 equations :
( - ( x - 4 ) ) = ( 7 - x ) + 1
( x - 4 ) = ( 7 - x ) + 1
( x - 4 ) = ( - ( 7 - x ) ) + 1
( - ( x - 4 ) ) = ( 7 - x ) + 1
- x + 4 = 7 - x + 1
- x + 4 = 8 - x
- x + x = 8 - 4
0 = 4
NO SOLUTION
( x - 4 ) = ( 7 - x ) + 1
x - 4 = 7 - x + 1
x - 4 = 8 - x
x + x = 8 + 4
2 x = 12 Divide both sides by 2
x = 12 / 2 = 6
( x - 4 ) = ( - ( 7 - x ) ) + 1
x - 4 = - 7 + x + 1
x - 4 = - 6 + x
x - x = - 6 + 4
0 = - 2
NO SOLUTION
Final solution :
x = 6
Thank you A LOT!