It is helpful if you're comfortable doing arithmetic with fractions. (If not, you can still work these problems, but you have to deal with fractions at some point.)
1) y + 4/9 - 1/9 = 7/9 . . . . . . . rearrange, use a common denominator
... y = 7/9 - 5/9
... y = 2/9
2) (2 1/2)x -(3/2)x -15/4 = 3/8
... x(5/2 -3/2) = 3/8 + 30/8 . . . . . . . consolidate x terms, add 15/4
... x = 33/8 . . . . . . . simplify
3) 0.9x + 1.26 - 2.3 + 0.1x = 1.6
... x - 1.04 = 1.6 . . . . . . . . . . . . . . simplify
... x = 2.64 . . . . . . . . . . . . . . . . . add 1.04
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If you want to eliminate fractions before you start, you can multiply by a suitable integer—usually the least common denominator.
1) Multiplying by 9 gives 6+9y-1=7; 5+9y=7; 9y=2; y=2/9
2) Multiplying by 8 gives 20x -6(2x+5)=3; 8x-30=3; 8x=33; x=33/8
3) Multiplying by 100 gives 9(10x+14) -230 +10x =160; 100x-104=160; 100x=264; x=2.64
