Question

Plz help ASAP, due friday -

Write the absolute value inequality in the form |x−b|c that has the solution set x≤−9 or x≥−5.

Answer 1

`\large\boxed\geq2`

Explanation:

Look at the picture.

`|x-a|\geq b\\\\a=(-9+(-5))/(2)=(-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\ :)`