Verified answer

[tex]\displaystyle \frac{4x+5}{8}\geq \frac{1-3x}{10}\\ \\5(4x+5)\geq 4(1-3x)\\ 20x+25\geq 4-12x\\20x+12x\geq 4-25\\32x\geq -21\\\\x\geq-\frac{21}{32}=x \in [-\frac{21}{32}, + \infty)[/tex]