The given inequality is
[tex]2 \ \lvert x +13\rvert \ \textless \ 9[/tex] ⇒ divide both sides over 2
∴ [tex]\lvert x +13\rvert \ \textless \ 4.5[/tex]
According to the absolute rules
x + 13 < 4.5 OR x + 13 > -4.5
║
x < 4.5 - 13 ║ x > -4.5 -13
║
x < -8.5 ║ x > -17.5
So, x ∈ (-17.5 , -8.5)
See the attached figures.
