Question

Which number line represents the solutions to [X-5]=1

Answer 1

second number line represents the [X-5]=1.

Explanation:

Given : [X-5]=1 .

To find : Which number line represents the solutions to [X-5]=1.

Solution : We have given that [X-5]=1.

We can se the value x-5 is inside the modulus it may be positive or negative.

So, we will do it by both cases.

1) (x - 5) = 1

On adding by 5 both sides.

x = 1+5 = 6

x = 6.

2) if -(x-5) = 1

remove parenthesis

-x +5 = 1

On subtracting by 5 both side

-x = -4

On dividing by -1 both side

x = 4.

So , x = 4, 6.

Therefore , second number line represents the [X-5]=1.

Answer 2

we have

`\left|x-5\right|=1`

Find the first solution (case positive)

`(x-5)=1`

Adds
`5` both sides

`(x-5)+5=1+5`

`x=6`

Find the second solution (case negative)

`-(x-5)=1`

`-x+5=1`

Adds
`(x-1)` both sides

`-x+5+x-1=1+x-1`

`x=4`

therefore

the answer in the attached figure