\(-\frac{2}{5}x-9<\frac{9}{10}\)
First, add 9 to both sides.
\(-\frac{2}{5}x<\frac{9}{10}+9\)
Simplify
\(-\frac{2}{5}x<\frac{99}{10}\)
Divide both sides by -2/5
\(x<\frac{\frac{99}{10}}{-\frac{2}{5}}\)
Anything divided by a fraction is the same as that number multiplied by the fraction's reciprocal.
\(x<\frac{99}{10}*-\frac{5}{2}\)
99*-5=-495
10*2=20
\(x<\frac{-495}{20}\)
Reduce.
\(\frac{-495}{20}=\frac{-99}{4}\)
That is the furthest it can simplify, so x>-99/4. If you want that in decimal form, here it is.
\(\frac{-99}{4}=-24.75\)
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