Question

How do you solve `abs(x-3)=2`?

Answer 1

`x = 1, 5`

Explanation:

`|x - 3| = 2`

`x - 3 = +-2`

`x - 3 = 2 => x = 5`
`x - 3 = -2 => x = 1`

Answer 2

`x=1" or "x=5`

Explanation:

`"the expression inside the absolute value can be positive"`
`"or negative, thus there are 2 possible solutions"`

`color(blue)"Positive"`

`x-3=2rArrx=2+3=5`

`color(blue)"Negative"`

`color(red)(-)(x-3)=2larrcolor(blue)"distribute"`

`-x+3=2`

`rArr-x=2-3=-1rArrx=1`

`color(blue)"As a check"`

`x=5to|5-3|=|2|=2larrcolor(blue)"True"`

`x=1to|1-3|=|-2|=2larrcolor(blue)"True"`

`rArrx=5" or "x=1" are the solutions"`