Find the value of x.

Solve for x:
-x/4 = 1/10

Multiply both sides of -x/4 = 1/10 by -4:
(-4 (-x))/4 = (-4)/10

(-4)/4 = (4 (-1))/4 = -1:
--1 x = (-4)/10

(-1)^2 = 1:
x = (-4)/10

Express -4/10 in its lowest form by cancelling out gcd(-4, 10) = 2 from the numerator and denominator. -4/10  =  (2 (-2))/(2×5)  =  -2/5:
Answer: |  x = (-2)/5

-x/3+x/4-x/6=1/10       multiply through by the common denominator of 3,4,6 and 10, i.e., 60

-20x  + 15x - 10x  =  6      combine like terms

-15x   = 6          divide both sides by -15

x = 6 / -15     =     -2 / 5