|1-0.3x|≥-3 is true for all x because all absolute values are positive, and all positive numbers are greater than all negative numbers. The same applies to y in |0.25y+5|>-0.75 and |4+2y|≥-3.
7-|3y-2|≤1 is the same as 6≤|3y-2| or |3y-2|≥6.
3y-2≥6, 3y≥8, y≥8/3; 2-3y≥6, -4≥3y, -4/3≥y, y≤-4/3. So y≥8/3 or y≤-4/3 is the solution.