what is 1/4x+5/2x=22?

multiply by 4
x+10x= 88
x=8

I am assuming 1/(4x) and 5/(2x)...
1/4x + 5/2x = 22 [get fractions in terms of same denominator]
1/4x + 10/4x = 22 [simplify]
11/4x = 22 [multiply both sides by 4x]
11 = 88x [divide both sides by 88]
11/88 = x [simplify]
x = 1/8

Do you mean 1/(4x) + 5/(2x) = 22 ?
Multiply by 4x:
1 + 10 = 88x
11 = 88x
x = 1/8

But if you meant (1/4)x + (5/2)x = 22.
multiply by 4:
x + 10x = 88
11x = 88
x = 8

Do you mean :-
(1/4)x + (5/2)x = 22 ?
x + 10x = 88
11x = 88
x = 8

Find a common denominator, 2*2=4, so you have 1/4x+10/4x=22. 22*4=88, so 1/4x+10/4x=88/4. Add the numerators on the left to get:

11x = 88
-------------
4

Since both sides have the same denominator, the fourths can go away, leaving:\

11x=88, and x=8.

Check 8/4+80/4=88/4

1/4x+5/2x=22
(1/4+5/2)x=22
11/4x=22
x=22(4/11)
x=8

(1/4)x + (5/2)x = 22

Multiply everything by 4 to get rid of the fractions
4*[(1/4)x + (5/2)x = 22]
(4/4)x + [(4*5)/2]x = 4*22
x + 10x = 88

Add x plux 10x
11x = 88

Divide both sides by 11 and the answer is
x = 8

(1/4)x + (5/2)x = 22
x/4 + 5x/2 = 22
4(x/4 + 5x/2) = 4(22)
x + 2(5x) = 88
x + 10x = 88
11x = 88
x = 88/11
x = 8