The sum of three fourths of a number and 1 is -5

We need to give the mystery number an easy name so that
we can work with it.  Let's call it it ' M ' , for 'mystery number'.

The number . . . . . . . . . . . . . M
3/4 of it . . . . . . . . . . . . . . . . . 3/4 M
the sum of 3/4 of it and 1 . . . (3/4 M + 1)

You said that sum is equal to  -5 .
OK.  The equation we need to solve is     

                                                 3/4 M + 1 = - 5

Subtract  1  from each side:      3/4 M      =  - 6

Multiply each side by  4 :          3    M      =  -24

Divide each side by  3 :                  M      =  -  8

Does it work ?

Check it :

-- Assume the mystery number is . . .  -8 .
-- 3/4 of the number . . . . . . . . . . . . .  - 6 .
-- sum of 3/4 of the number and 1 . . . -5  <==  yay !

40 & 50 in the right corner are the complementary angles as when placed in a sum (added together) they make 90°