To solve the inequality [tex]\( |4x + 16| > 8 \)[/tex], we need to consider two separate cases for the absolute value expression.
### Case 1: [tex]\( 4x + 16 > 8 \)[/tex]
1. Set up the inequality:
[tex]\[ 4x + 16 > 8 \][/tex]
2. Solve for [tex]\( x \)[/tex]:
[tex]\[ 4x + 16 - 16 > 8 - 16 \][/tex]
[tex]\[ 4x > -8 \][/tex]
[tex]\[ x > -2 \][/tex]
### Case 2: [tex]\( 4x + 16 < -8 \)[/tex]
1. Set up the inequality:
[tex]\[ 4x + 16 < -8 \][/tex]
2. Solve for [tex]\( x \)[/tex]:
[tex]\[ 4x + 16 - 16 < -8 - 16 \][/tex]
[tex]\[ 4x < -24 \][/tex]
[tex]\[ x < -6 \][/tex]
### Combine the results:
The solution to [tex]\( |4x + 16| > 8 \)[/tex] is:
[tex]\[ x < -6 \text{ or } x > -2 \][/tex]
Thus, the solution is:
[tex]\[ x < -6 \text{ or } x > -2 \][/tex]
