Question

Solve |x-4|>a if, case 1:a>0 and case 2 :a<0

Answer 1

we haven4t solution in second case

Answer 2

about first case
\[\left| x-4 \right|>a .... \left( x-4 \right)^{2}>a ^{2} ... x ^{2}+16-8x >a ^{2} ..... x ^{2} -8x >a ^{2} \]

Answer 3

Clearly for all real nos. the above graph is greater than 0.
So the answer for case 1 is R - {4} --- (4 is the point where we have an equality.)