Question #262189

Prove or disprove : for every real number x, |x − 8| + x ≥ 6.


1
Expert's answer
2021-11-10T15:47:35-0500

If x>8x>8 , then x8+x=x8+x=2x8>288=8|x-8|+x=x-8+x=2x-8>2\cdot 8-8=8 .

If x8x\leq 8 , then x8+x=8x+x=8|x-8|+x=8-x+x=8 .

We have that x8+x8| x-8|+x\geq 8 .

Since 8>68>6 , it follows that x8+x6|x-8|+x\geq 6 for every real number xx .


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