Question

How do you solve for x: `2|x − 3| + 4 = 6`?

Answer 1

`x=2" or "x=4`

Explanation:

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

`"isolate "|x-3|`

`"subtract 4 from both sides"`

`rArr2|x-3|=2`

`"divide both sides by 2"`

`rArr|x-3|=1`

`color(magenta)"Positive expression"`

`x-3=1rArrx=1+3=4`

`color(magenta)"Negative expression"`

`-(x-3)=1`

`rArr-x+3=1`

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

`color(blue)"As a check"`

Substitute these values into the left side and if equal to the right side then they are the solutions.

`x=2to2|-1|+4=(2xx1)+4=6`

`x=4to2|1|+4=(2xx1)+4=6`

`rArrx=2" or "x=4" are the solutions"`