Challenge 7: What values of x satisfy |x-4|+|x+4|<= 10.

Please give your response in intveral notation.

1 answer

|x-4| ≤ 10 - |x+4|
x-4 ≤ 10-|x+4| AND -x+4 ≤ 10 - |x+4)

|x+4 ≤ 14-x AND |x+4| ≤ 6 + x

x+4≤14-x AND -x-4 ≤ 14-x AND x+4 ≤ 6+x AND -x-4 ≤ 6+x

2x ≤ 10 AND -4 ≤ 14 AND 4 ≤ 6 AND -2x ≤ 10
x ≤ 5 AND x ≥ -5

The two inner statements are true, so we just use the outer two.

I don't use this "new" interval notation, I prefer

-5 ≤ x ≤ 5

I will let you change it to your notation.