How do you solve  sqrt(2x –3) = 2?

Apr 19, 2018

See below

Explanation:

Squaring both sides of equation we have

${\left(\sqrt{2 x - 3}\right)}^{2} = {2}^{2}$

$2 x - 3 = 4$

$2 x = 7$

$x = \frac{7}{2}$

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

Apr 19, 2018

$x = \frac{7}{2}$

Explanation:

$\textcolor{b l u e}{\text{square both sides}}$

${\left(\sqrt{2 x - 3}\right)}^{2} = {2}^{2}$

$\Rightarrow 2 x - 3 = 4$

$\text{add 3 to both sides and divide by 2}$

$\Rightarrow 2 x = 7 \Rightarrow x = \frac{7}{2}$

$\textcolor{b l u e}{\text{As a check}}$

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

$\sqrt{2 \times \frac{7}{2} - 3} = \sqrt{7 - 3} = \sqrt{4} = 2 = \text{ right side}$

$\Rightarrow x = \frac{7}{2} \text{ is the solution}$