ValkyrieRidn
Answered

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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].
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