The given inequality is,
[tex]|6x-5|<7[/tex]
According to absolute rule,
[tex]|y|0 then y>-a and y}Applying absolute rule to the given inequality, [tex]6x-5>-7\text{ and }6x-5<7[/tex]
Solving 6x-5>-7,
[tex]\begin{gathered} 6x-5>-7 \\ 6x>-7+5 \\ 6x>-2 \\ x>\frac{-2}{6} \\ x>\frac{-1}{3} \end{gathered}[/tex]
Solving 6x-5<7,
[tex]\begin{gathered} 6x-5<7 \\ 6x<7+5 \\ 6x<12 \\ x<\frac{12}{6} \\ x<2 \end{gathered}[/tex]
So, the solution is x>-1/3 and x<2.
The solution in interval notation is (-1/3, 2).
Now, the graph of the inequality is,
(Hollow dot in the graph indicates open interval).
