Question

How do you solve `sqrt(2x –3) = 2`?

Answer 1

See below

Explanation:

Squaring both sides of equation we have

`(sqrt(2x-3))^2=2^2`

`2x-3=4`

`2x=7`

`x=7/2`

Now check if it is a valid solution

`sqrt(2·7/2-3)=sqrt(7-3)=sqrt4=2`

Is a valid solution and our equation is now solved

Answer 2

`x=7/2`

Explanation:

`color(blue)"square both sides"`

`(sqrt(2x-3))^2=2^2`

`rArr2x-3=4`

`"add 3 to both sides and divide by 2"`

`rArr2x=7rArrx=7/2`

`color(blue)"As a check"`

Substitute this value into the left side of the equation and if equal to the right side then it is the solution.

`sqrt(2xx7/2-3)=sqrt(7-3)=sqrt4=2=" right side"`

`rArrx=7/2" is the solution"`