Question

Find all real solutions of the equation.

$5=\sqrt{4x-3}$

Short answer

The real solution of the given equation is $x=7$.

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:

$5=\sqrt{4x-3}$

Step 3. Solve the given equation.

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

$$\begin{gathered} {\left(5\right)}^2={\left(\sqrt{4x-3}\right)}^2 \\ 25=4x-3 \end{gathered}$$

Add$3$ on both sides.

$$\begin{gathered} 25+3=4x-3+3 \\ 28=4x \end{gathered}$$

Divide both sides by $4$.

role="math" localid="1643870637928" $\begin{array}{c}\frac{28}{4}=\frac{4x}{4}\\ 7=x\end{array}$

Thus, the real solution of the given equation is $x=7$.