we have the inequality
[tex]\mleft|2x-9\mright|<2[/tex]step 1
Find out the first solution (positive case)
[tex]\begin{gathered} +(2x-9)<2 \\ 2x<2+9 \\ 2x<11 \\ x<5.5 \end{gathered}[/tex]the first solution is the interval (-infinite, 5.5)
step 2
Find out tye second solution (negative case)
[tex]\begin{gathered} -(2x-9)<2 \\ mu\text{ltiply by -1 both sides} \\ 2x-9>-2 \\ 2x>\text{ -2+9} \\ 2x>7 \\ x>3.5 \end{gathered}[/tex]the second solution is the interval (3.5, infinite)
step 3
Find out the total solution
the solution is
(-infinite, 5.5) ∩ (3.5, infinite)=(3.5,5.5)