Find the solution set of $x$ satisfying the inequality $| 2 x + 7 | > 11$

$\displaystyle 2

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$\displaystyle -9

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x < 2

x > 9

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x < - 2

x>9$

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x < - 9

x > 2

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Solution

The correct option is E $x < - 9$ or $x > 2$
To find the solution we split the inequality $∣ 2 x + 7 ∣> 11$ in two inequality $∣ 2 x + 7 ∣> 11$ and $∣ 2 x + 7 ∣< - 11$
$\Rightarrow 2 x + 7 > 11$
$\Rightarrow 2 x > 11 - 7$
$\Rightarrow 2 x > 4$
$\Rightarrow x > 2$
$\Rightarrow 2 x + 7 < - 11$
$\Rightarrow 2 x < - 11 - 7$
$\Rightarrow 2 x < - 18$
$\Rightarrow x < - 9$
$∴ x < - 9$ or $x > 2$

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