Respuesta :

gmany

Answer:

[tex]\large\boxed{|x+7|\geq2}[/tex]

Step-by-step explanation:

Look at the picture.

[tex]|x-a|\geq b\\\\a=\dfrac{-9+(-5)}{2}=\dfrac{-14}{2}=-7\\\\b=-9-(-7)=-9+7=-2\\b=-5-(-7)=-5+7=2\\\\|x-(-7)|\geq2\\\\|x+7|\geq2\\\\Check:\\\\|x+7|\geq2\iff x+7\geq2\ \vee\ x+7\leq-2\qquad\text{subtract 7 from both sides}\\\\x+7-7\geq2-7\ \vee\ x+7-7\leq-2-7\\\\x\geq-5\ \vee\ x\leq-9\qquad CORRECT\ :)[/tex]

Ver imagen gmany

[tex]x \le -9 \ \text{ or } x \ge -5[/tex]

[tex]x \le -7 - 2 \ \text{ or } x \ge -7 + 2[/tex]

[tex]x+7 \le -7 - 2+7 \ \text{ or } x+7 \ge -7 + 2+7[/tex]

[tex]x+7 \le -2 \ \text{ or } x+7 \ge 2[/tex]

[tex]|x+7| \ge 2[/tex]

So the final answer is [tex]|x+7| \ge 2[/tex]

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side notes:

  • The -7 in step 2 is the midpoint of -9 and -5. You add up -9 and -5 to get -14, then divide by 2 to get -7.
  • x+7 is the same as x-(-7)
  • For the last step I used the rule that if |x| > k then x < -k or x > k for some positive number k

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