Question

Find all real solutions of the equation.

$\sqrt{2x-1}=\sqrt{3x-5}$

Short answer

The real solution of the given equation is $x=4$.

Step-by-step solution

Step 1. Definition of equation.

Equation is a mathematical statement in which two expressions are equal to each other.

Step 2. Given Information.

The given equation is:

$\sqrt{2x-1}=\sqrt{3x-5}$

Step 3. Solve the given equation.

Squaring both sides, the given equation can be rewritten as:

$$\begin{gathered} {\left(\sqrt{2x-1}\right)}^2={\left(\sqrt{3x-5}\right)}^2 \\ 2x-1=3x-5 \end{gathered}$$

Isolate the variable terms.

$$\begin{gathered} 2x-3x=-5+1 \\ -x=-4 \end{gathered}$$

Multiply both sides by $-1$.

role="math" localid="1643872087493" $$\begin{gathered} -x\times \left(-1\right)=-4\times \left(-1\right) \\ x=4 \end{gathered}$$

Thus, the real solution of the given equation is $x=4$.