Prove or disprove : for every real number x, |x − 8| + x ≥ 6.
If x>8x>8x>8 , then ∣x−8∣+x=x−8+x=2x−8>2⋅8−8=8|x-8|+x=x-8+x=2x-8>2\cdot 8-8=8∣x−8∣+x=x−8+x=2x−8>2⋅8−8=8 .
If x≤8x\leq 8x≤8 , then ∣x−8∣+x=8−x+x=8|x-8|+x=8-x+x=8∣x−8∣+x=8−x+x=8 .
We have that ∣x−8∣+x≥8| x-8|+x\geq 8∣x−8∣+x≥8 .
Since 8>68>68>6 , it follows that ∣x−8∣+x≥6|x-8|+x\geq 6∣x−8∣+x≥6 for every real number xxx .
Need a fast expert's response?
and get a quick answer at the best price
for any assignment or question with DETAILED EXPLANATIONS!
Comments