How do i solve ln l-3x-5l < 8

Question

Please help.

Answer 1

l-3x-5l < 8
write two cases
1. -3x - 5 < -8
2. -3x - 5 < 8
solve for case 1.
-3x - 5 < -8
add 5 to each side
-3x < -8
divide each side by 3
-x < -3/3
make x positive by reversing the inequality symbol
x > 1
solve for case 2
-3x - 5 < 8
add 5 to each side
-3x < 13
divide each side by 3
-x < 13/3
make x positive by reversing the inequality symbol
x > -13/3

Comments

Solution of the absolute inequality is -13/3 < x < 1 .

Answer 2

The absolute inequality is | - 3x - 5| < 8

|x| < a can be written as - a < x < a

| - 3x - 5| < 8 can be written as - 8 < - 3x - 5 < 8

Solve the inequality - 8 < - 3x - 5 < 8

- 8 + 5 < - 3x - 5 + 5 < 8 + 5

-3 < - 3x < 13

1 > x > -13/3

-13/3 < x < 1

Solution set is {x Є R| -13/3 < x < 1}

Observe the graph , the open circle means that -13/3 and 1 are not the solutions of the inequality.