Given the inequality:
[tex]|2x-9|\lt7[/tex]This is equivalent to:
[tex]-7\lt2x-9\lt7[/tex]We add 9 on each side of the inequality:
[tex]\begin{gathered} -7+9\lt2x-9+9\lt7+9 \\ 2\lt2x\lt16 \end{gathered}[/tex]Now, we divide by two:
[tex]\begin{gathered} \frac{2}{2}\lt\frac{2x}{2}\lt\frac{16}{2} \\ \\ 1\lt x\lt8 \end{gathered}[/tex]The answer is:
[tex]\lbrace x|x\gt1\text{ or }x\lt8\rbrace[/tex]
