Question

Solve the inequality. Graph the solution. 2 ∣ ∣ x+ 1 3 ∣ ∣ <9

Answer 1

The given inequality is

$2 \ \lvert x +13\rvert \ \textless \ 9$ ⇒ divide both sides over 2


∴  $\lvert x +13\rvert \ \textless \ 4.5$

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.