To solve the inequality [tex]\( |4w + 2| - 6 > 8 \)[/tex], let's go through it step-by-step:
1. Start with the given inequality:
[tex]\(|4w + 2| - 6 > 8\)[/tex]
2. Isolate the absolute value expression:
Add 6 to both sides:
[tex]\(|4w + 2| > 14\)[/tex]
3. Set up the compound inequality:
The inequality [tex]\(|4w + 2| > 14\)[/tex] means that the expression inside the absolute value is either greater than 14 or less than -14.
So we write two separate inequalities:
[tex]\[4w + 2 > 14\][/tex]
[tex]\[4w + 2 < -14\][/tex]
4. Solve each inequality separately:
For [tex]\(4w + 2 > 14\)[/tex]:
[tex]\[4w > 14 - 2\][/tex]
[tex]\[4w > 12\][/tex]
[tex]\[w > 3\][/tex]
For [tex]\(4w + 2 < -14\)[/tex]:
[tex]\[4w < -14 - 2\][/tex]
[tex]\[4w < -16\][/tex]
[tex]\[w < -4\][/tex]
5. Combine the results:
The solutions to the inequality [tex]\(|4w + 2| - 6 > 8\)[/tex] are:
[tex]\[w > 3 \quad \text{or} \quad w < -4\][/tex]
Therefore, the correct solution to the inequality is:
[tex]\[w > 3 \text{ or } w < -4\][/tex]
So, the correct answer from the given options is:
[tex]\[w > 3 \text{ or } w < -4\][/tex]
