We are given the following inequality
[tex]5(4x+1)<5_{}[/tex]Let us solve the above inequality for x.
Divide both sides of the inequality by 5
[tex]\begin{gathered} \frac{5(4x+1)}{5}<\frac{5_{}}{5} \\ 4x+1<1 \end{gathered}[/tex]Subtract 1 from both sides of the inequality
[tex]\begin{gathered} 4x+1-1<1-1 \\ 4x<0 \end{gathered}[/tex]Finally, divide both sides of the inequality by 4
[tex]\begin{gathered} \frac{4x}{4}<\frac{0}{4} \\ x<0 \end{gathered}[/tex]So, the solution is all the values less than 0 (0 is not included in the solution)
The solution in the interval notation is given by
[tex](-\infty,0)[/tex]