(1) 3.2b-9<1.4+0.6b.
Subtract 0.6b from each side:
2.6b-9<1.4.
Add 9 to each side:
2.6b<10.4.
Divide both sides by 2.6:
b<4. This means that b represents all numbers less than 4. Unlike an equation, an inequality doesn't have a single unique value as a solution. To solve an inequality you can add or subtract the same values from each side of the inequality sign and you can multiply or divide each side by a positive number (but not a negative number, because this affects the inequality sign). The idea of subtracting, adding, multiplying or dividing is to separate the known values from the unknown values (variables) so that you have unknowns on one side and knowns on the other. If you have variables on each side of the inequality you need to group them so that you can do arithmetic on them. The same applies to constants.
(2) 5(12-3w)>15w+60.
5, 15 and 60 are all multiples of 5, so divide both sides by 5:
12-3w>3w+12. 12 from each side
Subtract 12 from each side:
-3w>3w.
Add 3w to each side:
0>6w. Divide both sides by 6:
0>w. If zero is greater than w, then w must be less than 0, that is, w is negative. So w represents all negative numbers, w<0.
(3) 9x-(x-8)>x+29.
Remove the parentheses. This means the minus sign is distributed to what's inside the parentheses. The minus sign without a number after it simply means: multiply the contents of the parentheses by -1. So x becomes -x and -8 becomes +8: 9x-x+8>x+29.
This simplifies a little: 8x+8>x+29.
Subtract x from each side: 7x+8>29.
Subtract 8 from each side: 7x>21.
Divide both sides by 7: x>3. So x represents all the numbers greater than 3.