Solve and graph the absolute value inequality:

\[ |2x + 4| > 14 \]

14\\\\2x+4 > 14\ \vee\ 2x+4 < -14\\\\2x > 14-4\ \vee\ 2x < -14-4\\\\2x > 10\ \vee\ 2x < -18\\\\x > 5\ \vee\ x < -9\\\\see\ a\ picture\\\\x\in(-\infty;-9)\ \cup\ (5;\ \infty)"> ∣2 x + 4∣ > 14 2 x + 4 > 14 ∨ 2 x + 4 < − 14 2 x > 14 − 4 ∨ 2 x < − 14 − 4 2 x > 10 ∨ 2 x < − 18 x > 5 ∨ x < − 9 see a p i c t u re x ∈ ( − ∞ ; − 9 ) ∪ ( 5 ; ∞ )

Answered by Anonymous | 2024-06-10

|2x + 4| > 14 2x+ 4 = 14 2x + 4 = -14 x = 5 or x = - 9 2 5 = 10 +4 = 14 Yes 2 -9 = -18 + 4 = - 14 Yes 2x > 10 2x < - 18 X > 5 X < -9

Answered by UFGators | 2024-06-10

To solve the inequality 14"> ∣2 x + 4∣ > 14 , we find that the solutions are x < − 9 or 5"> x > 5 . The solution set is represented as intervals ( − ∞ , − 9 ) ∪ ( 5 , ∞ ) . We can graph this by shading the regions on a number line accordingly.
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Answered by Anonymous | 2024-09-11