Answer
$(-\infty, -\frac{1}{3})$
Refer to the attached image below for the graph.
Work Step by Step
For easier work, get rid of the fractions by multiplying the LCD of 5 to both sides to have:
$\\5(\frac{2}{5}x +1) \lt 5(\frac{1}{5}-2x)
\\2x+5 \lt 1-10x$
Add $10x$ to both sides to have:
$\\2x+5+10x \lt 1-10x+10x
\\12x+5 \lt 1$
Subtract 5 to both sides to have:
$\\12x+5-5 \lt 1 -5
\\12x \lt -4$
Divide 12 to both sides to have:
$\\x \lt \frac{-4}{12}
\\ x \lt -\frac{1}{3}$
