#### Answer

The solution is $\Big(-\dfrac{8}{5},\dfrac{2}{5}\Big)$

#### Work Step by Step

$\Big|\dfrac{3}{5}+x\Big|\lt1$
Solving this absolute value inequality is equivalent to solving the following inequality:
$-1\lt\dfrac{3}{5}+x\lt1$
Multiply the whole inequality by $5$:
$5\Big(-1\lt\dfrac{3}{5}+x\lt1\Big)$
$-5\lt3+5x\lt5$
Subtract $3$ from all three parts of the inequality:
$-5-3\lt3-3+5x\lt5-3$
$-8\lt5x\lt2$
Divide all three parts of the inequality by $5$:
$-\dfrac{8}{5}\lt\dfrac{5x}{5}\lt\dfrac{2}{5}$
Expressing the solution in interval notation:
$\Big(-\dfrac{8}{5},\dfrac{2}{5}\Big)$