Question

For what values of a are the following expressions true?

| a-5 | = 5-a

Answer 1

Question:-

what values of a are the following expressions true?

Expression :-

|a-5| =5-a

Answer:-

Try putting values of ( a )

1. Greater than 5
2. Less than 5
3. Equal to 5

First attempt :- Greater than 5

picking random number :-

Putting a = 6 :-

`|a-5| =5-a \\ |6-5| =5-6 \\ | 1| = -1 \\ 1 \cancel = ( - 1)`

so a is not equal to 6

Putting a = 8

`|a-5| =5-a \\ |8 - 5| =5-8 \\ |3| = - 3 \\ 3 \cancel = - 3`

a is also not equal to 8

so above values we can find a common result that a not equal to value bigger than 5

Second attempt :- Less than 5

picking random number

Putting a equal to 1

`|a-5| =5-a \\|1-5| =5-1 \\ | - 4| =4 \\ 4 = 4`

a can be equal to 1

Putting a equal to -3

`|a-5| =5-a \\| - 3-5| =5-( - 3) \\ | - 8| = 8\\ 8 = 8`

a can be equal to -3

So we can have a common result that a can be equal to values less than 5

Third attempt :- a equal to 5

putting a equal to 5

`|a-5| =5-a \\ |5 - 5| =5-5 \\ |0| =0 \\ 0 = 0`

So we can say a can be equal to 5

Result :- (a) can be equal to or less than 5