ValkyrieRidn
Answered

Get personalized and accurate responses to your questions with IDNLearn.com. Discover the reliable solutions you need with help from our comprehensive and accurate Q&A platform.

Solve the inequality:

[tex]\[
|2x + 10| \ \textgreater \ 6
\][/tex]

[tex]\[
x \ \textless \ [?] \text{ or } x \ \textgreater \ [?]
\][/tex]

Sagot :

GinnyAnsweridn
To solve the given inequality [tex]\(|2x + 10| > 6\)[/tex], let's break it down into two separate cases based on the properties of absolute values.

1. First Case: [tex]\(2x + 10 > 6\)[/tex]

- Start with the inequality [tex]\(2x + 10 > 6\)[/tex].
- To isolate [tex]\(x\)[/tex], first subtract 10 from both sides:
[tex]\[ 2x + 10 - 10 > 6 - 10 \][/tex]
[tex]\[ 2x > -4 \][/tex]
- Next, divide both sides by 2:
[tex]\[ x > -2 \][/tex]

2. Second Case: [tex]\(2x + 10 < -6\)[/tex]

- Start with the inequality [tex]\(2x + 10 < -6\)[/tex].
- To isolate [tex]\(x\)[/tex], first subtract 10 from both sides:
[tex]\[ 2x + 10 - 10 < -6 - 10 \][/tex]
[tex]\[ 2x < -16 \][/tex]
- Next, divide both sides by 2:
[tex]\[ x < -8 \][/tex]

Combining these two cases, we have the solution to the inequality [tex]\(|2x + 10| > 6\)[/tex]:

[tex]\[ x < -8 \quad \text{or} \quad x > -2 \][/tex]

Thus, the solution is [tex]\(x < -8\)[/tex] or [tex]\(x > -2\)[/tex].
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! Discover insightful answers at IDNLearn.com. We appreciate your visit and look forward to assisting you again.