I would really appreciate it, if someone helped me how to do this.

Question

│x-4│ - │7-x│ = 1

Answer 1

| 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

Answer 2

Thank you A LOT!