Respuesta :

tala32

[tex] |z - 1| = 7z - 13[/tex]
either:
[tex]z - 1 = 7z - 13[/tex]
and in that case:
[tex] - 1 + 13 = 7z - z[/tex]
[tex]12 = 6z[/tex]
[tex]z = 12 \div 6 = 2[/tex]
or:
[tex]z - 1 = - 7z + 13[/tex]
and in that case
[tex]z + 7z = 13 + 1[/tex]
[tex]8z = 14[/tex]
[tex]z = 14 \times 8 = 1.75[/tex]
So; the answer is: either 2 or 1.75
altavistard

Given:  |z-1| = 7z - 13

Due to the absolute value function, this equation yields two separate equations:

+(z-1) = 7z - 13, and

-(z-1) = 7z - 13.

Simplifying the first, we get z - 1 = 7z - 13, or

                                               -1 + 13 = 7z - z, or 12 = 6 z.  Then z = 2.

Doing the same to the 2nd equation:   -z + 1 = 7z - 13, or 14 = 8z, or z = 7/4.

We must check both results by subst. into  |z-1| = 7z - 13:

If z = 2, we get 2 - 1 = 14 - 13, or 1 = 1.  Thus, z = 2 is a solution.

If z = 7/4, we get 3/4 = 7(7/4) - 13, or   3/4 = 49/4 - 52.  This is clearly false.

The (single) solution is thus z = 2