ItNotJesusidn
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Solve the inequality:

[tex]\[ |4w + 2| - 6 \ \textgreater \ 8 \][/tex]

A. [tex]\( w \ \textgreater \ 3 \)[/tex]

B. [tex]\( -4 \ \textless \ w \ \textless \ 3 \)[/tex]

C. [tex]\( w \ \textgreater \ 3 \)[/tex] or [tex]\( w \ \textless \ -4 \)[/tex]

D. [tex]\( w \ \textgreater \ 3 \)[/tex] or [tex]\( w \ \textless \ -1 \)[/tex]

Sagot :

GinnyAnsweridn
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]
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