Question

the number of values of x satisfying |x-5|/x-5 > 2​

Answer 1

Answer

SOLUTION

TO CHOOSE THE CORRECT OPTION

complete values of X satisfying.

[x+5|+|6-x 1= 11

A. [-6, 5]

B. [5, 6]

C. [-5, 6]

D. [-6, 5]

EVALUATION

here the given equation is.

|x+5|+|6-x|= 11

here

|x+5|= 0 when x= -5

|6-x|= 0 when x= 6

Case: 1

when x <-5.

|x+5|+|6-x|

= -(x+5)+6-x]

= -x-5+6-x

= 1-2x

Case: 2

when -5≤ x≤6.

|x+5|+(6-x)

= x+5+6-x

= 11

Case: 3

when x >6

|x+5|+|6-x|

= (x+5)-(6-x)

= x+5-6+x

= 2x-1

Above three cases can rewritten as.

|x+5|+|6-x|= { 1-2x when x <-

{11 when -5

{2x-1 when x > 6

Hence |x+5+|6-x= 11 holds

when x € [-

FINAL ANSWER

Hence the correct option is.

C. [-5, 6]